75.8.5 problem 203

Internal problem ID [16821]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8. First order not solved for the derivative. Exercises page 67
Problem number : 203
Date solved : Tuesday, January 28, 2025 at 09:33:53 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 42

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

\begin{align*} y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to e^x \left (\int _1^xe^{-K[1]} K[1]dK[1]+c_1\right ) \\ \end{align*}