75.16.3 problem 476

Internal problem ID [16976]
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. Trial and error method. Exercises page 132
Problem number : 476
Date solved : Tuesday, January 28, 2025 at 09:44:03 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+3*diff(y(x),x)=exp(x),y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-3 x} \left (-3 \,{\mathrm e}^{3 x} c_{2} +c_{1} -\frac {3 \,{\mathrm e}^{4 x}}{4}\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 26

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

\[ y(x)\to \frac {e^x}{4}-\frac {1}{3} c_1 e^{-3 x}+c_2 \]