83.45.6 problem Ex 6 page 54

Internal problem ID [19478]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter IV. Equations of the first order but not of the first degree
Problem number : Ex 6 page 54
Date solved : Monday, March 31, 2025 at 07:19:59 PM
CAS classification : [_dAlembert]

\begin{align*} y&=\frac {x}{y^{\prime }}-a y^{\prime } \end{align*}

✓ Maple. Time used: 0.111 (sec). Leaf size: 391

ode:=y(x) = x/diff(y(x),x)-a*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} -\frac {c_1 \left (-y+\sqrt {4 a x +y^{2}}\right )}{\sqrt {\frac {-y+\sqrt {4 a x +y^{2}}+2 a}{a}}\, \sqrt {\frac {-y+\sqrt {4 a x +y^{2}}-2 a}{a}}}+x +\frac {\left (-y+\sqrt {4 a x +y^{2}}\right ) \left (-\ln \left (2\right )+\ln \left (\frac {\sqrt {2}\, \sqrt {\frac {y^{2}-y \sqrt {4 a x +y^{2}}-2 a^{2}+2 a x}{a^{2}}}\, a +\sqrt {4 a x +y^{2}}-y}{a}\right )\right ) \sqrt {2}}{2 \sqrt {\frac {y^{2}-y \sqrt {4 a x +y^{2}}-2 a^{2}+2 a x}{a^{2}}}} &= 0 \\ \frac {c_1 \left (y+\sqrt {4 a x +y^{2}}\right )}{2 \sqrt {\frac {-y-\sqrt {4 a x +y^{2}}+2 a}{a}}\, \sqrt {\frac {-y-\sqrt {4 a x +y^{2}}-2 a}{a}}}+x -\frac {\sqrt {2}\, \left (-\frac {3 \ln \left (2\right )}{2}+\ln \left (\frac {2 \sqrt {\frac {y \sqrt {4 a x +y^{2}}-2 a^{2}+2 a x +y^{2}}{a^{2}}}\, a -\left (y+\sqrt {4 a x +y^{2}}\right ) \sqrt {2}}{a}\right )\right ) \left (y+\sqrt {4 a x +y^{2}}\right )}{2 \sqrt {\frac {y \sqrt {4 a x +y^{2}}-2 a^{2}+2 a x +y^{2}}{a^{2}}}} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.765 (sec). Leaf size: 61

ode=y[x]==x/D[y[x],x]-a*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=\frac {a K[1] \arcsin (K[1])}{\sqrt {1-K[1]^2}}+\frac {c_1 K[1]}{\sqrt {1-K[1]^2}},y(x)=\frac {x}{K[1]}-a K[1]\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*Derivative(y(x), x) - x/Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out