75.8.3 problem 201

Internal problem ID [16819]
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 : 201
Date solved : Tuesday, January 28, 2025 at 09:33:47 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-2 x y^{\prime }-8 x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(x),x)^2-2*x*diff(y(x),x)-8*x^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 25

DSolve[D[y[x],x]^2-2*x*D[y[x],x]-8*x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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