77.1.87 problem 114 (page 172)

Internal problem ID [17977]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 114 (page 172)
Date solved : Tuesday, January 28, 2025 at 11:19:16 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.084 (sec). Leaf size: 14

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

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{c_{1} x} c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.107 (sec). Leaf size: 14

DSolve[y[x]*D[y[x],{x,2}]-D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 e^{c_1 x} \]