75.17.27 problem 577

Internal problem ID [17076]
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 : 577
Date solved : Tuesday, January 28, 2025 at 09:49:52 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-3*diff(y(x),x)=1+exp(x)+cos(x)+sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 5.370 (sec). Leaf size: 52

DSolve[D[y[x],{x,2}]-3*D[y[x],x]==1+Exp[x]+Cos[x]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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