75.3.4 problem 44

Internal problem ID [16701]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 3. The method of successive approximation. Exercises page 31
Problem number : 44
Date solved : Tuesday, January 28, 2025 at 09:18:40 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 10

dsolve([diff(y(x),x)=2*y(x)-2*x^2-3,y(0) = 2],y(x), singsol=all)
 

\[ y = x^{2}+x +2 \]

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 36

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

\[ y(x)\to e^{2 x} \left (\int _0^x-e^{-2 K[1]} \left (2 K[1]^2+3\right )dK[1]+2\right ) \]