29.33.4 problem 966

Internal problem ID [5543]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 966
Date solved : Monday, January 27, 2025 at 11:40:25 AM
CAS classification : [_rational]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 1.578 (sec). Leaf size: 131

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

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