75.2.9 problem 29

Internal problem ID [16686]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 09:18:01 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

\[ y = x^{2}+2 x +2+{\mathrm e}^{x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 31

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

\[ y(x)\to e^x \left (\int _1^x-e^{-K[1]} K[1]^2dK[1]+c_1\right ) \]