75.16.7 problem 480

Internal problem ID [16980]
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 : 480
Date solved : Tuesday, January 28, 2025 at 09:44:11 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }&=x \,{\mathrm e}^{\frac {3 x}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(4*diff(y(x),x$2)-3*diff(y(x),x)=x*exp(3/4*x),y(x), singsol=all)
 

\[ y = \frac {\left (9 x^{2}+72 c_{1} -24 x +32\right ) {\mathrm e}^{\frac {3 x}{4}}}{54}+c_{2} \]

✓ Solution by Mathematica

Time used: 4.638 (sec). Leaf size: 44

DSolve[D[y[x],{x,2}]-3*D[y[x],x]==x*Exp[3/4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{3 K[2]} \left (c_1+\int _1^{K[2]}e^{-\frac {9 K[1]}{4}} K[1]dK[1]\right )dK[2]+c_2 \]