75.18.1 problem 590

Internal problem ID [17089]
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 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 590
Date solved : Tuesday, January 28, 2025 at 09:51:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 9

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

\[ y = -2 x +2 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 10

DSolve[{D[y[x],{x,2}]+y[x]==2*(1-x),{y[0]==2,Derivative[1][y][0] ==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2-2 x \]