Internal problem ID [11264]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 50. Method
of undetermined coefficients. Page 107
Problem number: Ex 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=2 \,{\mathrm e}^{2 x} x -\sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*x*exp(2*x)-sin(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{2}+2 \left (x -2\right ) {\mathrm e}^{2 x}-\frac {3 \cos \left (2 x \right )}{50}-\frac {2 \sin \left (2 x \right )}{25}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 1.17 (sec). Leaf size: 53
DSolve[y''[x]-2*y'[x]+y[x]==2*x*Exp[2*x]-Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 e^{2 x} x-4 e^{2 x}-\frac {2}{25} \sin (2 x)-\frac {3}{50} \cos (2 x)+c_2 e^x x+c_1 e^x-\frac {1}{2} \]