Internal problem ID [13727]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 4.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 227
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)+5*diff(y(x),x)+y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x}}{5}+c_{1} {\mathrm e}^{\frac {\left (15 \sqrt {69}\, \left (404+60 \sqrt {69}\right )^{\frac {2}{3}}-101 \left (404+60 \sqrt {69}\right )^{\frac {2}{3}}-484 \left (404+60 \sqrt {69}\right )^{\frac {1}{3}}+1936\right ) x}{2904}}+c_{2} {\mathrm e}^{-\frac {\left (15 \sqrt {69}\, \left (404+60 \sqrt {69}\right )^{\frac {2}{3}}-101 \left (404+60 \sqrt {69}\right )^{\frac {2}{3}}-484 \left (404+60 \sqrt {69}\right )^{\frac {1}{3}}-3872\right ) x}{5808}} \cos \left (\frac {\left (404+60 \sqrt {69}\right )^{\frac {1}{3}} \sqrt {3}\, \left (15 \left (404+60 \sqrt {69}\right )^{\frac {1}{3}} \sqrt {69}-101 \left (404+60 \sqrt {69}\right )^{\frac {1}{3}}+484\right ) x}{5808}\right )+c_{3} {\mathrm e}^{-\frac {\left (15 \sqrt {69}\, \left (404+60 \sqrt {69}\right )^{\frac {2}{3}}-101 \left (404+60 \sqrt {69}\right )^{\frac {2}{3}}-484 \left (404+60 \sqrt {69}\right )^{\frac {1}{3}}-3872\right ) x}{5808}} \sin \left (\frac {\left (404+60 \sqrt {69}\right )^{\frac {1}{3}} \sqrt {3}\, \left (15 \left (404+60 \sqrt {69}\right )^{\frac {1}{3}} \sqrt {69}-101 \left (404+60 \sqrt {69}\right )^{\frac {1}{3}}+484\right ) x}{5808}\right ) \]
✓ Solution by Mathematica
Time used: 0.389 (sec). Leaf size: 2831
DSolve[y'''[x]-2*y''[x]+5*y'[x]+y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
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