77.1.78 problem 97 (page 135)

Internal problem ID [17968]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 97 (page 135)
Date solved : Tuesday, January 28, 2025 at 11:18:50 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y&=2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 81

dsolve(y(x)=2*diff(y(x),x)*x+x^2/2+diff(y(x),x)^2,y(x), singsol=all)
 

\begin{align*} y &= -\frac {x^{2}}{2} \\ y &= -\frac {1}{4} x^{2}+\frac {1}{2} c_{1} x +\frac {1}{4} c_{1}^{2} \\ y &= -\frac {1}{4} x^{2}-\frac {1}{2} c_{1} x +\frac {1}{4} c_{1}^{2} \\ y &= -\frac {1}{4} x^{2}-\frac {1}{2} c_{1} x +\frac {1}{4} c_{1}^{2} \\ y &= -\frac {1}{4} x^{2}+\frac {1}{2} c_{1} x +\frac {1}{4} c_{1}^{2} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]==2*D[y[x],x]*x+x^2/2+D[y[x],x]^2,y[x],x,IncludeSingularSolutions -> True]
 

Timed out