82.33.14 problem Ex. 14

Internal problem ID [18907]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 14
Date solved : Tuesday, January 28, 2025 at 12:34:10 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+n^{2} y&={\mathrm e}^{x} x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 129

dsolve(diff(y(x),x$2)+n^2*y(x)=exp(x)*x^4,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} \left (n^{2}+1\right )^{5} \cos \left (n x \right )+c_{2} \left (n^{2}+1\right )^{5} \sin \left (n x \right )+\left (120+n^{8} x^{4}+4 \left (x^{4}-2 x^{3}-3 x^{2}\right ) n^{6}+6 \left (x^{4}-4 x^{3}+2 x^{2}+16 x +4\right ) n^{4}+4 \left (x^{4}-6 x^{3}+15 x^{2}-60\right ) n^{2}+x^{4}-8 x^{3}+36 x^{2}-96 x \right ) {\mathrm e}^{x}}{\left (n^{2}+1\right )^{5}} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 115

DSolve[D[y[x],{x,2}]+n^2*y[x]==Exp[x]*x^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x \left (n^8 x^4+4 n^6 x^2 \left (x^2-2 x-3\right )+6 n^4 \left (x^4-4 x^3+2 x^2+16 x+4\right )+4 n^2 \left (x^4-6 x^3+15 x^2-60\right )+x^4-8 x^3+36 x^2-96 x+120\right )}{\left (n^2+1\right )^5}+c_1 \cos (n x)+c_2 \sin (n x) \]