Internal problem ID [15250]
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 ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 480.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {4 y^{\prime \prime }-3 y^{\prime }=x \,{\mathrm e}^{\frac {3 x}{4}}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {\left (9 x^{2}+72 c_{1} -24 x +32\right ) {\mathrm e}^{\frac {3 x}{4}}}{54}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.155 (sec). Leaf size: 35
DSolve[y''[x]-3*y'[x]==x*Exp[3/4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {16}{243} e^{3 x/4} (9 x-8)+\frac {1}{3} c_1 e^{3 x}+c_2 \]