75.8.4 problem 202

Internal problem ID [16820]
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 : 202
Date solved : Tuesday, January 28, 2025 at 09:33:48 AM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)^2+3*x*y(x)*diff(y(x),x)+2*y(x)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 26

DSolve[x^2*D[y[x],x]^2+3*x*y[x]*D[y[x],x]+2*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{x^2} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to 0 \\ \end{align*}