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Kamke differential equations. Mathematica and Maple. Earlier version

Nasser M.Abbasi

July 21, 2014

Contents


#1

 ′              1
y (x)− √a4x4+a3x3+a2x2+a1x+a0-=0

Maple

restart;  
ode1:=diff(y(x),x)-(a4*x^4+a3*x^3+a2*x^2+a1*x+a0)^(-1/2)=0;  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode1=y'[x]-1/Sqrt[(a4 x^4+a3 x^3+a2 x^2+a1 x+a0)]==0;  
DSolve[ode1,y,x]

PIC


#2

y′(x)+ ay(x) = cebx
Maple

restart;  
ode2:=diff(y(x),x)+a*y(x)=c*exp(b*x);  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode2=y'[x]+a y[x]-c Exp[b*x]==0  
DSolve[%,y[x],x]// TraditionalForm

PIC


#3

y′(x)+ ay(x) − bsin(cx)= 0
Maple

restart;  
ode3:=diff(y(x),x)+a*y(x)-b*sin(c*x)=0:  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode3=y'[x]+a y[x]-b Sin[c x]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#4

y′(x)+ 2xy(x) − xe−x2 = 0

Maple

restart;  
ode4:=diff(y(x),x)+2*x*y(x)-x*exp(-x^2)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode4=y'[x]+2 x y[x]-x Exp[-x^2]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#5

y′(x)+ y(x)cos(x)− e2x =0

Maple

restart;  
ode5:=diff(y(x),x)+y(x)*cos(x)-exp(2*x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode5=y'[x]+y[x] Cos[x]-Exp[2*x]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#6


Maple

restart;  
ode6:=diff(y(x),x)+y(x)*cos(x)-1/2*sin(2*x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode6=y'[x]+y[x] Cos[x]-1/2 Sin[2 x]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#7


Maple

restart;  
ode7:=diff(y(x),x)+y(x)*cos(x)-exp(-sin(x))=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode7=y'[x]+y[x] Cos[x]-Exp[-Sin[x]]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#8


Maple

restart;  
ode8:=diff(y(x),x)+y(x)*tan(x)-sin(2*x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode8=y'[x]+y[x] Tan[x]-Sin[2 x]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#9


Maple

restart;  
ode9:=diff(y(x),x)-(sin(log(x))+cos(log(x))+a)*y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode9=y'[x]-(Sin[Log[x]]+Cos[Log[x]]+a) y[x]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#10


Maple

restart;  
ode10:=diff(y(x),x)+diff(f(x),x)*y(x)=f(x)*diff(f(x),x);  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode10=y'[x]+f'[x]*y[x]-f[x]*f'[x]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#11


Maple

restart;  
ode11:=diff(y(x),x)+f(x)*y(x)=g(x);  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode11=y'[x]+f[x] y[x]==g[x];  
First[DSolve[%,y[x],x]]// TraditionalForm

PIC


#12


Maple

restart;  
ode12:=diff(y(x),x)+(y(x))^2=1:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode12=y'[x]+y[x]^2==1;  
DSolve[%,y[x],x]// TraditionalForm  
ExpToTrig[%]//FullSimplify// TraditionalForm

PIC


#13


Maple

restart;  
ode13:=diff(y(x),x)+(y(x))^2=a*x+b:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode13=y'[x]+y[x]^2==a x+b;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#14


Maple

restart;  
ode14:=diff(y(x),x)+(y(x))^2+a*x^m=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode14=y'[x]+y[x]^2+a x^m==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#15


Maple

restart;  
ode15:=diff(y(x),x)+(y(x))^2-2*x^2*y(x)+x^4-2*x-1=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode15 = y'[x] + y[x]^2 - 2 x^2 y[x] + x^4 - 2 x - 1 == 0;  
DSolve[%, y[x], x]// TraditionalForm

PIC


#16


Maple

restart;  
ode16:=diff(y(x),x)+y(x)^2- (x*y(x)-1)*f(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode16 = y'[x] + y[x]^2 + (x*y[x] - 1)*f[x] == 0;  
DSolve[%, y[x], x]

PIC


#17


Maple

restart;  
ode16:=diff(y(x),x)-y(x)^2- 3*y(x)+4=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode17 = y'[x] - y[x]^2 - 3*y[x] + 4 == 0;  
DSolve[%, y[x], x]// TraditionalForm

PIC


#18


Maple

restart;  
ode18:=diff(y(x),x)-y(x)^2- x*y(x)-x+1=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode18 = y'[x] - y[x]^2 - x*y[x] - x + 1 == 0;  
DSolve[%, y[x], x]// TraditionalForm

PIC


#19


Maple

restart;  
ode19:=diff(y(x),x)-(y(x)+x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode19=y'[x]-(y[x]+x)^2==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#20


Maple

restart;  
ode20:=diff(y(x),x)-y(x)^2+(x^2+1)*y(x)-2*x=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode20=y'[x]-y[x]^2+(x^2+1)*y[x]-2*x==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#21

y′(x)− y(x)2+ y(x)sin(x)− cos(x) =0

Maple

restart;  
ode21:=diff(y(x),x)-y(x)^2+y(x)*sin(x)-cos(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode21=y'[x]-y[x]^2+y[x]*Sin[x]-Cos[x]==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#22

y′(x)− y(x)2− y(x)sin(2x)− cos(2x)= 0

Maple

restart;  
ode22:=diff(y(x),x)-sin(2*x)*y(x)-y(x)^2=0;  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode22=y'[x]-y[x]^2-y[x]*Sin[2*x]-Cos[2*x]==0  
DSolve[%,y[x],x]

PIC


#23

 ′         2
y (x)+ ay(x) − b= 0

Maple

restart;  
ode23:=diff(y(x),x)+a*y(x)^2-b=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode23=y'[x]+a*y[x]^2-b==0;  
DSolve[%,y[x],x]// TraditionalForm

PIC


#24

 ′         2    ν
y (x)+ ay(x) − bx = 0

Maple

restart;  
ode24:=diff(y(x),x)+a*y(x)^2-b*x^nu=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode24=y'[x]+a*y[x]^2-b*x^nu==0;  
DSolve[%,y[x],x]//TraditionalForm

PIC


#25

y′(x)+ ay(x)2− bx2ν − cxν−1 = 0

Maple

restart;  
ode25:=diff(y(x),x)+a*y(x)^2-b*x^(2*nu)-c*x^(nu-1)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode25=y'[x]+a*y[x]^2-b*x^(2*\[Nu])-c*x^(\[Nu]-1)==0  
DSolve[%,y[x],x]// Simplify // TraditionalForm

PIC


#26


Maple

restart;  
ode26:=diff(y(x),x)-(A*y(x)-a)*(B*y(x)-b)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode26=y'[x]-(A*y[x]-a)*(B*y[x]-b)==0;  
DSolve[%,y[x],x]//TraditionalForm

PIC


#27


Maple

restart;  
ode27:=diff(y(x),x)+a*y(x)*(y(x)-x)-1=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode27=y'[x]+a*y[x]*(y[x]-x)-1==0;  
DSolve[%,y[x],x]//TraditionalForm

PIC


#28


Maple

restart;  
ode28:=diff(y(x),x)+x*y(x)^2-x^3*y(x)-2*x=0;  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode28=y'[x]+x*y[x]^2-x^3*y[x]-2*x==0;  
DSolve[%,y[x],x]//TraditionalForm

PIC


#29


Maple

restart;  
ode29:=diff(y(x),x)-x*y(x)^2-3*x*y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode29=y'[x]-x*y[x]^2-3*x*y[x]==0;  
DSolve[%,y[x],x]//TraditionalForm

PIC


#30


Maple

restart;  
ode30:=diff(y(x),x)+x^(-1-a)*y(x)^2-x^a=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode30=y'[x]+x^(-a-1)*y[x]^2-x^a==0  
DSolve[%,y[x],x]

PIC


#31


Maple

restart;  
ode31:=diff(y(x),x)-a*x^n*(y(x)^2+1)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode31 = y'[x] - a*x^n*(y[x]^2 + 1) == 0;  
DSolve[%, y[x], x] // TraditionalForm

PIC


#32


Maple

restart;  
ode31:=diff(y(x),x)+y(x)^2*sin(x)-2*sin(x)/cos(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode32=y'[x]+y[x]^2*Sin[x]-2*Sin[x]/Cos[x]^2==0;  
DSolve[%,y[x],x]//TraditionalForm

PIC


#33


Maple

restart;  
ode33:=diff(y(x),x)-y(x)^2*diff(f(x),x)/g(x)+diff(g(x),x)/f(x)=0;  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
(ode33=y'[x]-y[x]^2*D[f[x],x]/g[x]+D[g[x],x]/f[x]==0)//TraditionalForm  
DSolve[ode33,y[x],x]//TraditionalForm

PIC


#34


Maple

restart;  
ode34:=diff(y(x),x)+f(x)*y(x)^2+g(x)*y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode34=y'[x]+f[x]*y[x]^2+g[x]*y[x]==0  
DSolve[%,y[x],x]//TraditionalForm

PIC


#35


Maple

restart;  
ode35:=diff(y(x),x)+f(x)*(y(x)^2+2*a*y(x)+b)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode35 = y'[x] + f[x]*(y[x]^2 + 2*a*y[x] + b) == 0;  
DSolve[%, y[x], x] // TraditionalForm

PIC


#36


Maple

restart;  
ode36:=diff(y(x),x)+y(x)^3+a*x*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode36 = y'[x] + y[x]^3 + a*x*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#37


Maple

restart;  
ode37:=diff(y(x),x)-y(x)^3-a*exp(x)*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode37 = y'[x] - y[x]^3 - a*Exp[x]*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#38


Maple

restart;  
ode38:=diff(y(x),x)-a*y(x)^3-b*x^(3/2)=0:  
dsolve(%,y(x));

Nothing returned

Mathematica

Remove["Global‘*"]  
ode38 = y'[x] - a*y[x]^3 - b*x^(3/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#39


Maple

restart;  
ode39:=diff(y(x),x)-a3*y(x)^3-a2*y(x)^2-a1*y(x)-a0=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode39 = y'[x] - a3*y[x]^3 - a2*y[x]^2 - a1*y[x] - a0 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#40


Maple

restart;  
ode40:=diff(y(x),x)+3*a*y(x)^3+6*a*x*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode40 = y'[x] + 3*a*y[x]^3 + 6*a*x*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#41

y′(x)+ axy(x)3+ by(x)2 = 0

Maple

restart;  
ode41:=diff(y(x),x)+a*x*y(x)^3+b*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode41 = y'[x] + a*x*y[x]^3 + b*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#42

y′(x)− x(x+ 2)y(x)3− (x+ 3)y(x)2 = 0

Maple

restart;  
ode42:=diff(y(x),x)-x*(x+2)*y(x)^3-(x+3)*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode42 = y'[x] - x*(x + 2)*y[x]^3 - (x + 3)*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#43

 ′        2    2        3       2
y (x)+ (3ax + 4a x+ b)y (x) + 3xy(x) = 0

Maple

restart;  
ode43:=diff(y(x),x)+(3*a*x^2+4*a^2*x+b)*y(x)^3+3*x*y(x)^2=0:  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode43 = y'[x] + (3*a*x^2 + 4*a^2*x + b)*y[x]^3 + 3*x*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#44

 ′       3    3
y (x)+ 2ax y(x) + 2xy(x) = 0

Maple

restart;  
ode44:=diff(y(x),x)+2*a*x^3*y(x)^3+2*x*y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode44 = y'[x] + 2*a*x^3*y[x]^3 + 2*x*y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#45

y′(x)+ 2(a2x3− b2x)y(x)3+ 3by(x)2 =0

Maple

restart;  
ode45:=diff(y(x),x)+2*(a^2*x^3-b^2*x)*y(x)^3+3*b*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode45 = y'[x] + 2*(a^2*x^3 - b^2*x)*y[x]^3 + 3*b*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#46


Maple

restart;  
ode46:=diff(y(x),x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1)=0:  
dsolve(%,y(x));

PIC Mathematica

Remove["Global‘*"]  
ode46=y'[x]-x^a*y[x]^3+3*y[x]^2-x^(-a)*y[x]-x^(-2*a)+a*x^(-a-1)==0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#47


Maple

restart;  
ode47:=diff(y(x),x)-a*(x^n-x)*y(x)^3-y(x)^2=0:  
dsolve(%,y(x));

No output

Mathematica

Remove["Global‘*"]  
ode47 = y'[x] - a*(x^n - x)*y[x]^3 - y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#48


Maple

restart;  
ode48:=diff(y(x),x)-(a*x^n+b*x)*y(x)^3-c*y(x)^2=0:  
dsolve(%,y(x));

No output
Mathematica

Remove["Global‘*"]  
ode48 = y'[x] - (a*x^n + b*x)*y[x]^3 - c*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#49


Maple

restart;  
ode49:=diff(y(x),x)+a*diff(phi(x),x)*y(x)^3+6*a*phi(x)*y(x)^2+(2*a+1)*y(x)*diff(phi(x),x$2)/diff(phi(x),x)+2*a+2=0;  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode49 = y'[x] + a*phi'[x]*y[x]^3 +  
   6*a*phi[x]*y[x]^2 + (2*a + 1)*y[x]*phi''[x]/phi'[x] + 2*a + 2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#50


Maple

restart;  
ode50:=diff(y(x),x)-f3(x)*y(x)^3-f2(x)*y(x)^2-f1(x)*y(x)-f0(x)=0;  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode50 = y'[x] - f3[x]*y[x]^3 - f2[x]*y[x]^2 - f1[x]*y[x] - f0[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#51


Maple

restart;  
ode51:=diff(y(x),x)-(y(x)-f(x))*(y(x)-g(x))*(y(x)-(a*f(x)+b*g(x))/(a+b))*h(x)-  
diff(f(x),x)*(y(x)-g(x))/(f(x)-g(x))-diff(g(x),x)*(y(x)-f(x))/(g(x)-f(x))=0;  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode51 = D[y[x],x] - (y[x] - f[x])*(y[x] -g[x])*(y[x] - (a*f[x] + b*g[x])/(a + b))*h[x] -  
   D[f[x], x]*(y[x] - g[x])/(f[x] - g[x])-D[g[x], x]*(y[x] - f[x])/(g[x] - f[x]) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#52


Maple

restart;  
ode52:=diff(y(x),x)-b*x^(n/(1-n))-a*y(x)^n=0;  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode52 = D[y[x], x] - a*y[x]^n - b*x^(n/(1 - n)) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#53


Maple

restart;  
ode53:=diff(y(x),x)-(y(x)*diff(f(x),x))/f(x)-f(x)*diff(g(x),x)-  
f(x)^(1-n)/(b+a*g(x))^n*y(x)^n*diff(g(x),x)=0;  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode53 = y'[x] - f[x]^(1 - n)*g'[x]*y[x]^n/(a*g[x] + b)^n -  
   f'[x]*y[x]/f[x] - f[x]*g'[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#54


Maple

restart;  
ode54:=diff(y(x),x)-a^n*f(x)^(1-n)*diff(g(x),x)*y(x)^n-(diff(f(x),x)*y(x))/f(x)-f(x)*diff(g(x),x)=0:  
dsolve(%,y(x));

PIC
Mathematica

Remove["Global‘*"]  
ode54=y'[x]-a^n*f[x]^(1-n)*g'[x]*y[x]^n-f'[x]*y[x]/f[x]-f[x]*g'[x]==0  
DSolve[%,y[x],x]//TraditionalForm

PIC


#55


Maple

restart;  
ode55:=diff(y(x),x)-f(x)*y(x)^n-g(x)*y(x)-h(x)=0:  
dsolve(%,y(x));

No answer

Mathematica

Remove["Global‘*"]  
ode55 = y'[x] - f[x]*y[x]^n - g[x]*y[x] - h[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#56

 ′            a          b
y (x)− f(x)y(x)− g(x)y(x) = 0
Maple

restart;  
ode56:=diff(y(x),x)-f(x)*y(x)^a-g(x)*y(x)^b=0:  
dsolve(%,y(x));

No answer

Mathematica

Remove["Global‘*"]  
ode56=y'[x]-f[x]*y[x]^a-g[x]*y[x]^b==0  
DSolve[%,y[x],x]//TraditionalForm

PIC


#57

 ′     ∘-----
y (x)−  |y(x)|= 0
Maple

restart;  
ode57:=diff(y(x),x)-sqrt(abs(y(x)))=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode57=y'[x]-Abs[y[x]]^(1/2)==0  
DSolve[%,y[x],x]//TraditionalForm

PIC


#58

           1
y′(x)− ay(x)2 − bx = 0
Maple

restart;  
ode58:=diff(y(x),x)-a*y(x)^(1/2)-b*x=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode58 = y'[x] - a*y[x]^(1/2) - b*x == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#59

y′(x)− a(y(x)2+ 1)12 − b= 0
Maple

restart;  
ode59:=diff(y(x),x)-a*(y(x)^2+1)^(1/2)-b=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode59 = y'[x] - a*(y[x]^2 + 1)^(1/2) - b == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#60

 ′     (y(x)2−1)12-
y (x)−  (x2−1)12 = 0
Maple

restart;  
ode60:=diff(y(x),x)-(y(x)^2-1)^(1/2)/(x^2-1)^(1/2)=0:  
dsolve(%,y(x));  

PIC

Mathematica

Remove["Global‘*"]  
ode60 = y'[x] - (y[x]^2 - 1)^(1/2)/(x^2 - 1)^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#61

        (x2−1)12
y′(x)− (y(x)2−1)12-= 0
Maple

restart;  
ode61:=diff(y(x),x)-(x^2-1)^(1/2)/(y(x)^2-1)^(1/2)=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode61 = y'[x] - (x^2 - 1)^(1/2)/(y[x]^2 - 1)^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#62

 ′     y(x)−x2√x2−y(x)2
y (x)− x+xy(x)√x2−y(x)2-= 0
Maple

restart;  
ode62:=diff(y(x),x)-(y(x)-x^2*(x^2-y(x)^2)^(1/2))/(x+x*y(x)*(x^2-y(x)^2)^(1/2))=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"]  
ode62 = D[y[x],x] - (y[x] -  
       x^2*(x^2 - y[x]^2)^(1/2))/(x*y[x]*(x^2 - y[x]^2)^(1/2) + x)==0;  
DSolve[%, y[x], x] // TraditionalForm

PIC


#63

y′(x)− -----1||+y(x)2√-----||= 0
       (1+x)3∕2||y(x)+  1+y(x)||
Maple

restart;  
ode63:=diff(y(x),x)-(1+y(x)^2)/((1+x)^(3/2)*abs(y(x)+sqrt(1+y(x))))=0:  
dsolve(%,y(x));

PIC

Mathematica

Remove["Global‘*"];  
ode63 = D[y[x],x]-(y[x]^2 + 1)/(Abs[y[x]+(1+y[x])^(1/2)]*(1+x)^(3/2))==0  
DSolve[%, y[x], x] // TraditionalForm

No answer after 10 minutes wait


#64

       ∘-----------
y′(x)−   c+bcy+(xb)+x+aayx(x2)2= 0
Maple

restart;  
ode64:=diff(y(x),x)-sqrt((c+b*y(x)+a*y(x)^2)/(c+b*x+a*x^2))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode64 =D[y[x], x] - ((a*y[x]^2 + b*y[x] + c)/(a*x^2 + b*x + c))^(1/2)==0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#65


Maple

restart;  
ode65:=diff(y(x),x)-sqrt((1+y(x)^3)/(1+x^3))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode65 = D[y[x], x] - ((y[x]^3 + 1)/(x^3 + 1))^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#66


Maple

restart;  
ode66:=diff(y(x),x)-sqrt((abs((1-y(x))*y(x)*(1-a*y(x))))/(abs((1-x)*x*(1-a*x))))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode66=D[y[x],x]-Abs[y[x]*(1-y[x])*(1-a*y[x])]^(1/2)/Abs[x*(1-x)*(1-a*x)]^(1/2)==0  
DSolve[%,y[x],x]//TraditionalForm

No answer after 10 minutes wait. Abort
PIC


#67


Maple

restart;  
ode67:=diff(y(x),x)-sqrt((1-y(x)^4)/(1-x^4))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode67 = D[y[x], x] - (1 - y[x]^4)^(1/2)/(1 - x^4)^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#68


Maple

restart;  
ode68:=diff(y(x),x)-sqrt((1+b*y(x)^2+a*y(x)^4)/(1+b*x^2+a*x^4))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode68 = D[y[x],x]-((a*y[x]^4 + b*y[x]^2 + 1)/(a*x^4 + b*x^2 + 1))^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#69


Maple

restart;  
ode69:=diff(y(x),x)-sqrt((a0+a1*x+a2*x^2+a3*x^3+a4*x^4)*(b0+b1*y(x)+b2*y(x)^2+b3*y(x)^3+b4*y(x)^4))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode69=D[y[x],x]-((b4*y[x]^4+b3*y[x]^3+b2*y[x]^2+b1*y[x]+b0)*  
       (a4*x^4+a3*x^3+a2*x^2+a1*x+a0))^(1/2)==0  
DSolve[%,y[x],x]//TraditionalForm

PIC


#70


Maple

restart;  
ode70:=diff(y(x),x)-sqrt((a0+a1*x+a2*x^2+a3*x^3+a4*x^4)/(b0+b1*y(x)+b2*y(x)^2+b3*y(x)^3+b4*y(x)^4))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode70=D[y[x],x]-((a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0)/(b4*y[x]^4 +  
      b3*y[x]^3 + b2*y[x]^2 + b1*y[x] + b0))^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#71


Maple

restart;  
ode71:=diff(y(x),x)-sqrt((b0+b1*y(x)+b2*y(x)^2+b3*y(x)^3+b4*y(x)^4)/(a0+a1*x+a2*x^2+a3*x^3+a4*x^4))=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode71 = D[y[x],x] - ((b4*y[x]^4 + b3*y[x]^3 + b2*y[x]^2 + b1*y[x] + b0)/(a4*x^4 +  
         a3*x^3 + a2*x^2 + a1*x + a0))^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#72


Maple

restart;  
ode72:=diff(y(x),x)-R1(x,sqrt(a0+a1*x+a2*x^2+a3*x^3+a4*x^4))*  
R2(y(x),sqrt(b0+b1*y(x)+b2*y(x)^2+b3*y(x)^3+b4*y(x)^4))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode72 = D[y[x], x] -R1[x, (a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0)^(1/2)]*  
    R2[y[x], (b4*y[x]^4 + b3*y[x]^3 + b2*y[x]^2 + b1*y[x] + b0)^(1/2)] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#73


Maple

restart;  
ode73:=diff(y(x),x)-((a0+a1*x+a2*x^2+a3*x^3)/(a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3))^(2/3)=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode73=D[y[x],x]-((a3*x^3+a2*x^2+a1*x+a0)/(a3*y[x]^3+a2*y[x]^2+a1*y[x]+a0))^(2/3)==0  
DSolve[%,y[x],x]//TraditionalForm

PIC


#74


Maple

restart;  
ode74:=diff(y(x),x)-f(x)*sqrt((-a*y(x))*(-b*y(x)))*(y(x)-g(x))=0;  
dsolve(%,y(x));

Not solved
PIC

Mathematica

Clear["Global‘*"];  
ode74 = D[y[x], x]-f[x]*(y[x] - g[x])*((y[x] - a)*(y[x] - b))^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

Not solved
PIC


#75


Maple

restart;  
ode75:=diff(y(x),x)+exp(x)-exp(x-y(x))=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode75=D[y[x],x]-Exp[x-y[x]]+Exp[x]==0  
DSolve[%,y[x],x]//TraditionalForm

PIC


#76


Maple

restart;  
ode76:=diff(y(x),x)+b-a*cos(y(x))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode76 = D[y[x], x] - a*Cos[y[x]] + b == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#77


Maple

restart;  
ode77:=diff(y(x),x)-cos(b*x+a*y(x))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode77 = D[y[x], x] - Cos[a*y[x] + b*x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#78


Maple

restart;  
ode78:=diff(y(x),x)+a* sin(alpha *y(x)+ beta*x)+b=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode78=D[y[x],x]+a*Sin[\[Alpha] y[x]+\[Beta]*x]+b==0  
DSolve[%,y[x],x]//TraditionalForm

PIC


#79


Maple

restart;  
ode79:=diff(y(x),x)+f(x)*cos(a*y(x))+g(x)*sin(a*y(x))+h(x)=0;  
dsolve(%,y(x));

No solution
PIC

Mathematica

Clear["Global‘*"];  
ode79=D[y[x],x]+f[x]*Cos[a*y[x]]+g[x]*Sin[a*y[x]]+h[x]==0  
DSolve[%,y[x],x]//TraditionalForm

No solution
PIC


#80

y′(x)+ f(x)sin(y(x))+ (1− f′(x))cos(y (x))− f′(x) − 1 = 0
Maple

restart;  
ode80:=diff(y(x),x)+f(x)*sin(y(x))+(1-diff(f(x),x))*cos(y(x))-diff(f(x),x)-1=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode80 = D[y[x], x] + f[x]*Sin[y[x]] + (1 - D[f[x], x])*Cos[y[x]] -  
   D[f[x], x] - 1 == 0  
DSolve[%, y[x], x] // TraditionalForm

No solution
PIC


#81

y′(x)+ 2tan (y (x))tan (x) − 1 = 0
Maple

restart;  
ode81:=diff(y(x),x)+2*tan(y(x))*tan(x)-1=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode81 = D[y[x], x] + 2*Tan[y[x]]*Tan[x] - 1 == 0  
DSolve[%, y[x], x] // TraditionalForm

No solution
PIC


#82

 ′      (           2)
y (x)− a 1+ tan (y(x)) + tan(y(x))tan(x)= 0
Maple

restart;  
ode82:=diff(y(x),x)-a*(1+tan(y(x))^2)+tan(y(x))*tan(x)=0;  
dsolve(%,y(x));

No solution
PIC

Mathematica

Clear["Global‘*"];  
ode82 = D[y[x], x] - a*(1 + Tan[y[x]]^2) + Tan[y[x]]*Tan[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

No solution
PIC


#83

 ′
y (x)− tan(xy(x))= 0
Maple

restart;  
ode83:=diff(y(x),x)-tan(x*y(x))=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode83 = D[y[x], x] - Tan[x*y[x]] == 0  
DSolve[%, y[x], x] // TraditionalForm

No solution
PIC


#84

y′(x)− f(ax+ by(x))= 0
Maple

restart;  
ode84:=diff(y(x),x)-f(a*x+b*y(x))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode84 = D[y[x], x] - f[a*x + b*y[x]] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#85


Maple

restart;  
ode85:=diff(y(x),x)-x^(a-1)*y(x)^(1-b)*f(x^a/a+y(x)^b/b)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode85 = D[y[x], x] - x^(a - 1)*y[x]^(1 - b)*f[x^a/a + y[x]^b/b] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#86


Maple

restart;  
ode86:=diff(y(x),x)-((-x*f(x^2+a*y(x)^2)+y(x))/(x+a*f(x^2+a*y(x)^2)*y(x)))=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode86 = D[y[x],x]-(y[x]-x*f[x^2 + a*y[x]^2])/(x+a*y[x]*f[x^2+a*y[x]^2])==0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#87


Maple

restart;  
ode87:=diff(y(x),x)-((a*f(x^c*y(x))*y(x)+c*x^a*y(x)^b)/(b*x*f(x^c*y(x))-x^a*y(x)^b))=0;  
dsolve(%,y(x));

no solution
PIC

Mathematica

Clear["Global‘*"];  
ode87 = D[y[x],x]-(y[x]*a*f[x^c*y[x]]+c*x^a*y[x]^b)/(x*b*f[x^c*y[x]]-x^a*y[x]^b)== 0  
DSolve[%, y[x], x] // TraditionalForm

no solution
PIC


#88


Maple

restart;  
ode88:=2*diff(y(x),x)-b-c*exp(-2*a*x)-4*a*y(x)-3*y(x)^2=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode88 = 2*D[y[x], x] - 3*y[x]^2 - 4*a*y[x] - b - c*Exp[-2*a*x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#89


Maple

restart;  
ode89:=x*diff(y(x),x)-sqrt(a^2-x^2)=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode89 = x*D[y[x], x] - (a^2 - x^2)^(1/2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#90


Maple

restart;  
ode90:=x*diff(y(x),x)+y(x)-x*sin(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode90 = x*D[y[x], x] + y[x] - x*Sin[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#91


Maple

restart;  
ode91:=x*diff(y(x),x)-y(x)-x/log(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode91 = x*D[y[x], x] - y[x] - x/Log[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#92


Maple

restart;  
ode92:=x*diff(y(x),x)-y(x)-x^2*sin(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode92 = x*D[y[x], x] - y[x] - x^2*Sin[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#93


Maple

restart;  
ode93:=x*diff(y(x),x)-y(x)-(x*cos(log(log(x))))/(log(x))=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode93 = x*D[y[x], x] - y[x] - x*Cos[Log[Log[x]]]/Log[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#94


Maple

restart;  
ode94:=x*diff(y(x),x)+b*x^n+a*y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode94 = x*D[y[x], x] + a*y[x] + b*x^n == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#95


Maple

restart;  
ode95:=x*diff(y(x),x)+x^2+y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode95 = x*D[y[x], x] + y[x]^2 + x^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#96


Maple

restart;  
ode96:=x*diff(y(x),x)+1-y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode96 = x*D[y[x], x] - y[x]^2 + 1 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#97


Maple

restart;  
ode97:=x*diff(y(x),x)+b*x^2-y(x)+a*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode97 = x*D[y[x], x] + a*y[x]^2 - y[x] + b*x^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#98


Maple

restart;  
ode98:=x*diff(y(x),x)+c*x^(2*b)-b*y(x)+a*y(x)^2=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode98 = x*D[y[x], x] + a*y[x]^2 - b*y[x] + c*x^(2*b) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#99


Maple

restart;  
ode99:=x*diff(y(x),x)-c*x^beta-b*y(x)+a*y(x)^2=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode99 = x*D[y[x], x] + a*y[x]^2 - b*y[x] - c*x^\[Beta] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#100

xy′(x)+ a+ xy(x)2 =0
Maple

restart;  
ode100:=x*diff(y(x),x)+a+x*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode100 = x*D[y[x], x] + x*y[x]^2 + a == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#101

xy′(x)− y(x)+xy (x)2 = 0
Maple

restart;  
ode101:=x*diff(y(x),x)-y(x)+x*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode101 = x*D[y[x], x] + x*y[x]^2 - y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#102

  ′       3            2
xy (x)− ax − y (x)+ xy(x) = 0
Maple

restart;  
ode102:=x*diff(y(x),x)-a*x^3-y(x)+x*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode102 = x*D[y[x], x] + x*y[x]^2 - y[x] - a*x^3 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#103

  ′      3       2           2
xy (x)− x − (1 +2x )y(x)+ xy(x)= 0
Maple

restart;  
ode103:=x*diff(y(x),x)-x^3-(1+2*x^2)*y(x)+x*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode103 = x*D[y[x], x] + x*y[x]^2 - (2*x^2 + 1)*y[x] - x^3 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#104

xy′(x)+ bx + 2y (x)+ axy(x)2 = 0
Maple

restart;  
ode104:=x*diff(y(x),x)+b*x+2*y(x)+a*x*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode104 = x*D[y[x], x] + a*x*y[x]^2 + 2*y[x] + b*x == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#105


Maple

restart;  
ode105:=x*diff(y(x),x)+d+c*x+b*y(x)+a*x*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode105 = x*D[y[x], x] + a*x*y[x]^2 + b*y[x] + c*x + d == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#106


Maple

restart;  
ode106:=x*diff(y(x),x)+x^b+(1/2)*(a-b)*y(x)+x^a*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode106 = x*D[y[x], x] + x^a*y[x]^2 + 1/2*(a - b)*y[x] + x^b == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#107


Maple

restart;  
ode107:=x*diff(y(x),x)-c*x^beta+b*y(x)+a*x^alpha*y(x)^2=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode107 = x*D[y[x], x] + a*x^\[Alpha]*y[x]^2 + b*y[x] - c*x^\[Beta] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#108


Maple

restart;  
ode108:=x*diff(y(x),x)-y(x)^2*log(x)+y(x)=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode108 = x*D[y[x], x] - y[x]^2*Log[x] + y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#109


Maple

restart;  
ode109:=x*diff(y(x),x)-y(x)*(2*log(x)*y(x)-1)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode109 = x*D[y[x], x] - y[x]*(2*y[x]*Log[x] - 1) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#110


Maple

restart;  
ode110:=x*diff(y(x),x)-f(x)*(y(x)^2-x^2)=0:  
dsolve(%,y(x));

did not solve

Mathematica

Clear["Global‘*"];  
ode110 = x*D[y[x], x] + f[x]*(y[x]^2 - x^2) == 0  
DSolve[%, y[x], x] // TraditionalForm

did not solve


#111


Maple

restart;  
ode111:=x*diff(y(x),x)+y(x)^3+3*x*y(x)^2=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode111 = x*D[y[x], x] + y[x]^3 + 3*x*y[x]^2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#112


Maple

restart;  
ode112:=x*diff(y(x),x)-y(x)-sqrt(x^2+y(x)^2)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode112 = x*D[y[x], x] - (y[x]^2 + x^2)^(1/2) - y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#113


Maple

restart;  
ode113:=x*diff(y(x),x)-y(x)+a*sqrt(x^2+y(x)^2):  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode113 = x*D[y[x], x] + a*(y[x]^2 + x^2)^(1/2) - y[x] == 0  
DSolve[%, y[x], x]

PIC


#114


Maple

restart;  
ode114:=x*diff(y(x),x)-x*sqrt(y(x)^2+x^2)-y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode114 = x*D[y[x], x] - x*(y[x]^2 + x^2)^(1/2) - y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#115


Maple

restart;  
ode115:=x*diff(y(x),x)-y(x)-x*(y(x)-x)*sqrt(x^2+y(x)^2)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode115 = x*D[y[x], x] - x*(y[x] - x)*(y[x]^2 + x^2)^(1/2) - y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#116


Maple

restart;  
ode116:=x*diff(y(x),x)-y(x)-x*sqrt((y(x)^2-4*x^2)*(y(x)^2-x^2))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode116 = x*D[y[x], x]-x*((y[x]^2 - x^2)*(y[x]^2-4*x^2))^(1/2)-y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#117


Maple

restart;  
ode117:=x*diff(y(x),x)-x-x*exp(y(x)/x)-y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode117 = x*D[y[x], x] - x*Exp[y[x]/x] - y[x] - x == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#118


Maple

restart;  
ode118:=x*diff(y(x),x)-y(x)*log(y(x))=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode118 = x*D[y[x], x] - y[x]*Log[y[x]] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#119


Maple

restart;  
ode119:=x*diff(y(x),x)-y(x)*(log(x*y(x))-1)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode119 = x*D[y[x], x] - y[x]*(Log[x*y[x]] - 1) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#120

xy′(x)− y(x)(2+ xln ( x2-))= 0
                    y(x)
Maple

restart;  
ode120:=x*diff(y(x),x)-y(x)*(2+x*log(x^2/y(x)))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode120 = x*D[y[x], x] - y[x]*(x*Log[x^2/y[x]] + 2) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#121

  ′
xy (x)+ sin(y(x)− x)= 0
Maple

restart;  
ode121:=x*diff(y(x),x)+sin(y(x)-x)=0;  
dsolve(%,y(x));

Did not solve
PIC

Mathematica

Clear["Global‘*"];  
ode121 = x*D[y[x], x] + Sin[y[x] - x] == 0  
DSolve[%, y[x], x] // TraditionalForm

Did not solve
PIC


#122

xy′(x)+ cos(y(x))(sin (y (x))− 3x2cos(y(x))) =0
Maple

restart;  
ode122:=x*diff(y(x),x)+cos(y(x))*(sin(y(x))-3*x^2*cos(y(x)))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode122 = x*D[y[x], x] + (Sin[y[x]] - 3*x^2*Cos[y[x]])*Cos[y[x]] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#123

           (   )
xy′(x)− xsin y(xx) − y(x)= 0
Maple

restart;  
ode123:=x*diff(y(x),x)-y(x)-x*sin(y(x)/x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode123 = x*D[y[x], x] - x*Sin[y[x]/x] - y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#124

xy′(x)+ xcos(y(xx) ) − y (x)+ x =0
Maple

restart;  
ode124:=x*diff(y(x),x)+x*cos(y(x)/x)-y(x)+x=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode124 = x*D[y[x], x] + x*Cos[y[x]/x] - y[x] + x == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#125


Maple

restart;  
ode125:=x*diff(y(x),x)+x*tan(y(x)/x)-y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode125 = x*D[y[x], x] + x*Tan[y[x]/x] - y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#126
Maple

restart;  
ode126:=x*diff(y(x),x)-y(x)*f(x*y(x))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode126 = x*D[y[x], x] - y[x]*f[x*y[x]] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#127


Maple

restart;  
ode127:=x*diff(y(x),x)-f(x^a*y(x)^b)*y(x)=0;  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode127 = x*D[y[x], x] - y[x]*f[x^a*y[x]^b] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#128


Maple

restart;  
ode128:=x*diff(y(x),x)-f(x)*g(x^a*y(x))+a*y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode128 = x*D[y[x], x] + a*y[x] - f[x]*g[x^a*y[x]] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#129


Maple

restart;  
ode129:=(1+x)*diff(y(x),x)+y(x)*(y(x)-x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode129 = (1 + x)*D[y[x], x] + y[x]*(y[x] - x) == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#130


Maple

restart;  
ode130:=2*x*diff(y(x),x)-2*x^3-y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode130 = 2*x*D[y[x], x] - y[x] - 2*x^3 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#131


Maple

restart;  
ode131:=(1+2*x)*diff(y(x),x)+2-4*exp(-y(x))=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode131 = (2*x + 1)*D[y[x], x] - 4*Exp[-y[x]] + 2 == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#132


Maple

restart;  
ode132:=3*x*diff(y(x),x)-y(x)-3*x*log(x)*y(x)^4=0:  
dsolve(%,y(x));  

PIC

Mathematica

Clear["Global‘*"];  
ode132 = 3*x*D[y[x], x] - 3*x*Log[x]*y[x]^4 - y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#133


Maple

restart;  
ode133:=x^2*diff(y(x),x)+y(x)=x:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode133 = x^2*D[y[x], x] + y[x] == x  
DSolve[%, y[x], x] // TraditionalForm

PIC


#134


Maple

restart;  
ode134:=x^2*diff(y(x),x)-y(x)=-x^2*exp(x - 1/x):  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode134 = x^2*D[y[x], x] - y[x] == -x^2*Exp[x - 1/x]  
DSolve[%, y[x], x] // TraditionalForm

PIC


#135


Maple

restart;  
ode135:=x^2*diff(y(x),x)-(x-1)*y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode135 = x^2*D[y[x], x] - (-1 + x)*y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#136


Maple

restart;  
ode136:=x^2*diff(y(x),x)+x*y(x)+y(x)^2=-x^2:  
dsolve(%,y(x));  

PIC

Mathematica

Clear["Global‘*"];  
ode136 = x^2*D[y[x], x] + y[x]^2 + x*y[x] == -x^2  
DSolve[%, y[x], x] // TraditionalForm

PIC


#137


Maple

restart;  
ode137:=x^2*diff(y(x),x)-y(x)^2-x*y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode137 = x^2*D[y[x], x] - y[x]^2 - x*y[x] == 0  
DSolve[%, y[x], x] // TraditionalForm

PIC


#138
Maple

restart;  
ode138:=x^2*diff(y(x),x)-y(x)^2-x*y(x)=x^2:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode138 = x^2*D[y[x], x] - y[x]^2 - x*y[x] == x^2  
DSolve[%, y[x], x] // TraditionalForm

PIC


#139
Maple

restart;  
ode139:=x^2*(y(x)^2+diff(y(x),x))=-a*x^k+b*(b-1):  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode139 = x^2*(D[y[x], x] + y[x]^2) == -a*x^k + b*(b - 1)  
DSolve[%, y[x], x] // TraditionalForm

PIC


#140 x2(y′(x)+ y(x)2)= − 4xy (x)− 2
Maple

restart;  
ode140:=x^2*(y(x)^2+diff(y(x),x))=-4*x*y(x)-2:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode140 = x^2*(D[y[x], x] + y[x]^2) == -4*x*y[x] - 2  
DSolve[%, y[x], x] // TraditionalForm

PIC


#141 x2(y′(x)+ y(x)2)+ axy(x)= −b
Maple

restart;  
ode141:=x^2*(y(x)^2+diff(y(x),x))+a*x*y(x)=-b:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode141 = x^2*(D[y[x], x] + y[x]^2) + a*x*y[x] == -b  
DSolve[%, y[x], x] // TraditionalForm

PIC


#142  2 ′        2     2
x (y(x)− y(x))− ax y(x)= −ax− 2
Maple

restart;  
ode142:=x^2*(-y(x)^2+diff(y(x),x))-a*x^2*y(x)=-2-a*x:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode142 = x^2*(D[y[x], x] - y[x]^2) - a*x^2*y[x] == -a*x - 2  
DSolve[%, y[x], x] // TraditionalForm

PIC


#143  2(    2   ′   )
x  ay(x) +y (x) = b
Maple

restart;  
ode143:=x^2*(a*y(x)^2+diff(y(x),x))=b:  
dsolve(%,y(x));

PIC

Mathematica

Clear["Global‘*"];  
ode143 = x^2*(D[y[x], x] + a*y[x]^2) == b  
DSolve[%, y[x], x] // TraditionalForm

PIC


#144   (            )
x2 ay(x)2 +y′(x) +c +bxα =0
Maple 17

restart;  
ode144:=x^2*(a*y(x)^2+diff(y(x),x))+b*x^alpha+c=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode144 = x^2*(D[y[x], x] + a*y[x]^2) + b*x^\[Alpha] + c == 0  
DSolve[%, y[x], x]

PIC


#145 − ax2y2(x)+ay3(x)+ x2y′(x)= 0
Maple 17

restart;  
ode145:=-a*x^2*y(x)^2+a*y(x)^3+x^2*diff(y(x),x)=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode145 = x^2*D[y[x], x] + a*y[x]^3 - a*x^2*y[x]^2 == 0  
DSolve[%, y[x], x]

PIC


#146
Maple 17.01

restart;  
ode146:=x^2*diff(y(x),x)+a*y(x)^2+x*y(x)^3=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode146 = x^2*D[y[x], x] + x*y[x]^3 + a*y[x]^2 == 0  
DSolve[%, y[x], x]

PIC


#147
Maple 17.01

restart;  
ode147:=a*x^2*y(x)^3+b*y(x)^2+x^2 * diff(y(x),x)=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode147 = x^2*D[y[x], x] + a*x^2*y[x]^3 + b*y[x]^2 == 0;  
DSolve[%, y[x], x]

PIC


#148
Maple 17.01

restart;  
ode148:=(x^2+1)* diff(y(x),x)+x*y(x)-1=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode148 = (x^2 + 1)*D[y[x], x] + x*y[x] - 1 == 0;  
DSolve[%, y[x], x]

PIC


#149
Maple 17.01

restart;  
ode149:=(x^2+1)* diff(y(x),x)-x *(x^2+1)+x *y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode149 = (x^2 + 1)*D[y[x], x] + x*y[x] - x*(x^2 + 1) == 0;  
DSolve[%, y[x], x]

PIC


#150
Maple 17.01

restart;  
ode150:=(x^2+1)* diff(y(x),x)-2* x^2+2* x* y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode150 = (x^2 + 1)*D[y[x], x] + 2*x*y[x] - 2*x^2 == 0;  
DSolve[%, y[x], x]

PIC


#151
Maple 17.01

restart;  
ode151:=(x^2+1)* diff(y(x),x)+(2* x *y(x)-1)* (y(x)^2+1)=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode151 = (x^2 + 1)*D[y[x], x] + (y[x]^2 + 1)*(2*x*y[x] - 1) == 0;  
DSolve[%, y[x], x]

PIC


#152
Maple 17.01

restart;  
ode152:=(x^2+1)*diff(y(x),x)-x * (x^2+1)* cos(y(x))^2+x* sin(y(x)) *cos(y(x))=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode152 = (x^2 + 1)*D[y[x], x] + x*Sin[y[x]]*Cos[y[x]] -  
    x*(x^2 + 1)*Cos[y[x]]^2 == 0;  
DSolve[%, y[x], x]

PIC


#153
Maple 17.01

restart;  
ode153:=a+(x^2-1)* diff(y(x),x)-x* y(x)=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode153 = (x^2 - 1)*D[y[x], x] - x*y[x] + a == 0;  
DSolve[%, y[x], x]

PIC


#154
Maple 17.01

restart;  
ode154:=(x^2-1)* diff(y(x),x)+2* x *y(x)-cos(x)=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode154 = (x^2 - 1)*D[y[x], x] + 2*x*y[x] - Cos[x] == 0;  
DSolve[%, y[x], x]

PIC


#155
Maple 17.01

restart;  
ode155:=(x^2-1)*diff(y(x),x)+y(x)^2-2* x* y(x)+1=0:  
dsolve(%,y(x));

PIC

Mathematica 9.01

Clear["Global‘*"];  
ode155 = (x^2 - 1)*D[y[x], x] + y[x]^2 - 2*x*y[x] + 1 == 0;  
DSolve[%, y[x], x]

PIC