75.6.2 problem 126

Internal problem ID [16758]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 126
Date solved : Tuesday, January 28, 2025 at 09:21:24 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

dsolve([x^2-x*diff(y(x),x)=y(x),y(1) = 0],y(x), singsol=all)
 

\[ y = \frac {x^{3}-1}{3 x} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 17

DSolve[{x^2-x*D[y[x],x]==y[x],{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3-1}{3 x} \]