Internal problem ID [10265]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-4 y^{\prime }-x^{2}+3 \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(x),x$3)-4*diff(y(x),x)=x^2-3*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-2 x} c_{2}}{2}+\frac {{\mathrm e}^{2 x} c_{1}}{2}-\frac {x^{3}}{12}-\frac {3 x \,{\mathrm e}^{2 x}}{8}+\frac {9 \,{\mathrm e}^{2 x}}{32}-\frac {x}{8}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 49
DSolve[y'''[x]-4*y'[x]==x^2-3*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{24} x \left (2 x^2+3\right )+\frac {1}{32} e^{2 x} (-12 x+9+16 c_1)-\frac {1}{2} c_2 e^{-2 x}+c_3 \\ \end{align*}