77.1.97 problem 124 (page 179)

Internal problem ID [17987]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 124 (page 179)
Date solved : Tuesday, January 28, 2025 at 08:28:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }&=4 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 87

dsolve(x^2*y(x)*diff(y(x),x$2)+x^2*diff(y(x),x)^2-5*x*y(x)*diff(y(x),x)=4*y(x)^2,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= -\frac {x^{3-\sqrt {17}} 17^{{3}/{4}} \sqrt {-\left (x^{2 \sqrt {17}} c_{1} -c_{2} \right ) x^{-3+\sqrt {17}}}}{17} \\ y &= \frac {x^{3-\sqrt {17}} 17^{{3}/{4}} \sqrt {-\left (x^{2 \sqrt {17}} c_{1} -c_{2} \right ) x^{-3+\sqrt {17}}}}{17} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.899 (sec). Leaf size: 39

DSolve[x^2*y[x]*D[y[x],{x,2}]+x^2*D[y[x],x]^2-5*x*y[x]*D[y[x],x]==4*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^{\frac {3}{2}-\frac {\sqrt {17}}{2}} \sqrt {x^{2 \sqrt {17}}+c_1} \]