75.14.9 problem 335

Internal problem ID [16923]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 335
Date solved : Tuesday, January 28, 2025 at 09:41:00 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {1}{3} x^{3}+\frac {1}{2} c_{1} x^{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 24

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

\[ y(x)\to \frac {x^3}{3}+\frac {c_1 x^2}{2}+c_2 \]