15.19.10 problem 10

Internal problem ID [3294]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:31:34 AM
CAS classification : [_quadrature]

\begin{align*} y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (x^{2}+y^{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 48

dsolve(y(x)*diff(y(x),x)^2+(y(x)^2-x^3-x*y(x)^2)*diff(y(x),x)-x*y(x)*(x^2+y(x)^2)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= {\mathrm e}^{-x} c_{1} \\ y \left (x \right ) &= \sqrt {{\mathrm e}^{x^{2}} c_{1} -x^{2}-1} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{x^{2}} c_{1} -x^{2}-1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 15.082 (sec). Leaf size: 61

DSolve[y[x]*D[y[x],x]^2+(y[x]^2-x^3-x*y[x]^2)*D[y[x],x]-x*y[x]*(x^2+y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-x} \\ y(x)\to -\sqrt {-x^2+c_1 e^{x^2}-1} \\ y(x)\to \sqrt {-x^2+c_1 e^{x^2}-1} \\ \end{align*}