Internal problem ID [11279]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52.
Summary. Page 117
Problem number: Ex 5.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime }=x^{2}-3 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(diff(y(x),x$3)-4*diff(y(x),x)=x^2-3*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (9-12 x +16 c_{1} \right ) {\mathrm e}^{2 x}}{32}-\frac {x^{3}}{12}-\frac {{\mathrm e}^{-2 x} c_{2}}{2}-\frac {x}{8}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.311 (sec). Leaf size: 49
DSolve[y'''[x]-4*y'[x]==x^2-3*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^3}{12}-\frac {x}{8}+\frac {1}{32} e^{2 x} (-12 x+9+16 c_1)-\frac {1}{2} c_2 e^{-2 x}+c_3 \]