75.17.4 problem 554

Internal problem ID [17053]
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. Superposition principle. Exercises page 137
Problem number : 554
Date solved : Tuesday, January 28, 2025 at 09:47:47 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=\left (1+\sin \left (x \right )\right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=(1+sin(x))*exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.205 (sec). Leaf size: 71

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

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