Internal problem ID [11298]
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 15.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y=x \,{\mathrm e}^{x}+\cos \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 121
dsolve(diff(y(x),x$3)-y(x)=x*exp(x)+cos(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\cos \left (2 x \right )}{10 \left (5+2 \sqrt {3}\right ) \left (-5+2 \sqrt {3}\right )}+\frac {4 \sin \left (2 x \right )}{5 \left (5+2 \sqrt {3}\right ) \left (-5+2 \sqrt {3}\right )}-\frac {13 \left (3 \,{\mathrm e}^{x} x^{2}-6 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{x}-9\right )}{18 \left (5+2 \sqrt {3}\right ) \left (-5+2 \sqrt {3}\right )}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 7.274 (sec). Leaf size: 98
DSolve[y'''[x]-y[x]==x*Exp[x]+Cos[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x x^2}{6}-\frac {e^x x}{3}+\frac {2 e^x}{9}-\frac {4}{65} \sin (2 x)-\frac {1}{130} \cos (2 x)+c_1 e^x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_3 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )-\frac {1}{2} \]