Internal problem ID [4838]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }=9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)-2*diff(y(x),x)=9*x*exp(-x)-6*x^2+4*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (4 x +c_{1} -2\right ) {\mathrm e}^{2 x}}{2}+\left (3 x +4\right ) {\mathrm e}^{-x}+x^{3}+\frac {3 x^{2}}{2}+\frac {3 x}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.492 (sec). Leaf size: 49
DSolve[y''[x]-2*y'[x]==9*x*Exp[-x]-6*x^2+4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x \left (2 x^2+3 x+3\right )+e^{-x} (6 x+8)+e^{2 x} (4 x-2+c_1)\right )+c_2 \]