29.33.3 problem 965

Internal problem ID [5542]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 965
Date solved : Monday, January 27, 2025 at 11:36:14 AM
CAS classification : [_rational]

\begin{align*} x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \end{align*}

✗ Solution by Maple

dsolve(x*y(x)*diff(y(x),x)^2+(a+x^2-y(x)^2)*diff(y(x),x)-x*y(x) = 0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.390 (sec). Leaf size: 112

DSolve[x y[x] (D[y[x],x])^2+(a+x^2-y[x]^2)D[y[x],x]-x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sqrt {c_1 \left (x^2+\frac {a}{1+c_1}\right )} \\ y(x)\to -\sqrt {\left (\sqrt {a}-i x\right )^2} \\ y(x)\to \sqrt {\left (\sqrt {a}-i x\right )^2} \\ y(x)\to -\sqrt {\left (\sqrt {a}+i x\right )^2} \\ y(x)\to \sqrt {\left (\sqrt {a}+i x\right )^2} \\ \end{align*}