3.9.24 Problems 2301 to 2400

Table 3.553: First order ode linear in derivative

#

ODE

Mathematica

Maple

4786

y=yxtan(yx)

4787

(1+x)y+y1x2+2x3=0

4788

y=xy22yx1x3

4789

y=2y2x+yx2x

4790

y=exy2+yex

4864

x2yxy=1x

4865

xln(y)yyln(x)=0

4868

2xysin(2x)=(sin(x)22y)y

4870

3x3y2yx2y3=1

4872

y2yy2e3x=0

4873

u(v+1)+v2(1u)u=0

4874

y+2xxy=0

4880

(y+2x)yx+2y=0

4881

(xcos(y)esin(y))y+1=0

4882

sin(x)2y+sin(x)2+(x+y)sin(2x)=0

4884

y+xy=xy

4886

sin(θ)cos(θ)rsin(θ)2=rcos(θ)2

4888

3x2y+x3y=0

4889

y+xy=x2

4893

xy=xy+y

4895

y=3x2y

4897

xy=y

4912

ysin(x+y)=0

4913

y=4y23y+1

4914

s=tln(s2t)+8t2

4915

y=yex+yx2+2

4916

(xy2+3y2)y2x=0

4917

s2+s=s+1st

4918

xy=1y3

4919

x=3xt2

4920

x=tet2xx

4921

y=xy21+x

4922

xv=14v23v

4923

y=sec(y)2x2+1

4924

y=3x2(1+y2)32

4925

xx3=x

4926

x+xy2+ex2yy=0

4927

yy+yecos(x)sin(x)=0

4928

y=(1+y2)tan(x)

4929

y=x3(1y)

4930

y2=y+1cos(x)

4931

x2y=4x2x2(1+x)(y+1)

4932

yθ=ysin(θ)y2+1

4933

x2+2yy=0

4934

y=2tcos(y)2

4935

y=8x3e2y

4936

y=x2(y+1)

4937

y+(1+x)y=0

4938

y=ex2

4939

y=ex2y2

4940

y=sin(x)+1(1+y2)

4941

y=2y2ty

4942

y=y13

4943

y=y13

4944

y=(x3)(y+1)23

4945

y=xy3

4946

y=xy3

4947

y=xy3

4948

y=xy3

4949

y=y23y+2

4950

x2y+sin(x)y=0

4951

x+xt=ex

4952

(t2+1)y=tyy

4953

3t=ety+yln(t)

4954

xx+xt2=sin(t)

4955

3r=rθ3

4956

yye3x=0

4957

y=yx+2x+1

4958

r+rtan(θ)=sec(θ)

4959

xy+2y=1x3

4960

t+y+1y=0

4961

y=x2e4x4y

4962

yy+2x=5y3

4963

xy+3x2+3y=sin(x)x

4964

(x2+1)y+xyx=0

4965

(x2+1)yx2y=(1+x)x2+1

4966

yyx=xex

4967

y+4yex=0

4968

t2x+3xt=t4ln(t)+1

4969

y+3yx+2=3x

4970

cos(x)y+ysin(x)=2xcos(x)2

4971

ysin(x)+cos(x)y=xsin(x)

4972

y+y1+sin(x)2=x

4973

(e4y+2x)y1=0

4974

y+2y=xy2

4975

y+3yx=x2

4976

x=αβcos(πt12)kx

4977

u=α(1u)βu

4978

x2y+x4cos(x)x3y=0

4979

x1032y+xy=0

4980

2yy2+(x2+2x+3)y=0

4981

yexy+2x+(xexy2y)y=0

4982

y+xy=0

4983

y2+(2xy+cos(y))y=0

4984

2x+ycos(xy)+(xcos(xy)2y)y=0

4985

θr+3rθ1=0

4986

2xy+3+(x21)y=0

4987

2x+y+(x2y)y=0

4988

exsin(y)3x2+(excos(y)+13y23)y=0

4989

cos(x)cos(y)+2x(sin(x)sin(y)+2y)y=0