75.16.75 problem 548

Internal problem ID [17048]
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 : 548
Date solved : Tuesday, January 28, 2025 at 09:47:33 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

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

\[ y = -\frac {{\mathrm e}^{x} \left (-8 x^{2} c_{3} -8 c_{2} x +\sin \left (2 x \right )-8 c_{1} -2 x \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 80

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

\[ y(x)\to e^x \left (x^2 \int _1^x\frac {1}{2} \cos (2 K[3])dK[3]+x \int _1^x-\cos (2 K[2]) K[2]dK[2]+\int _1^x\frac {1}{2} \cos (2 K[1]) K[1]^2dK[1]+c_3 x^2+c_2 x+c_1\right ) \]