75.16.61 problem 534

Internal problem ID [17034]
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 : 534
Date solved : Tuesday, January 28, 2025 at 09:47:06 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=4 \,{\mathrm e}^{x} \left (\sin \left (x \right )+\cos \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)+2*diff(y(x),x)=4*exp(x)*(sin(x)+cos(x)),y(x), singsol=all)
 

\[ y = -\frac {\left (\frac {4 \left (\cos \left (x \right )-3 \sin \left (x \right )\right ) {\mathrm e}^{3 x}}{5}-2 \,{\mathrm e}^{2 x} c_{2} +c_{1} \right ) {\mathrm e}^{-2 x}}{2} \]

✓ Solution by Mathematica

Time used: 5.554 (sec). Leaf size: 48

DSolve[D[y[x],{x,2}]+2*D[y[x],x]==4*Exp[x]*(Sin[x]+Cos[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-2 K[2]} \left (c_1+\int _1^{K[2]}4 e^{3 K[1]} (\cos (K[1])+\sin (K[1]))dK[1]\right )dK[2]+c_2 \]