Internal problem ID [10246]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 48. Page
103
Problem number: Ex 4.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+5*diff(y(x),x)-2*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{2}-\frac {5}{4}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 34
DSolve[y'''[x]-4*y''[x]+5*y'[x]-2*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (-\frac {1}{2}+c_2 e^x\right )+e^x \left (c_3 e^x+c_1\right )-\frac {5}{4} \\ \end{align*}