82.45.2 problem Ex. 2

Internal problem ID [18970]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 100
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:41:06 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}-m^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 101

dsolve(diff(y(x),x$5)-m^2*diff(y(x),x$3)=exp(a*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {2 c_{1} \left (-a^{5}+a^{3} m^{2}\right ) {\mathrm e}^{-m x}+2 c_{2} \left (a^{5}-a^{3} m^{2}\right ) {\mathrm e}^{m x}+m^{3} \left (2 \,{\mathrm e}^{a x}+a^{3} \left (a -m \right ) \left (a +m \right ) \left (c_3 \,x^{2}+2 c_4 x +2 c_5 \right )\right )}{2 a^{5} m^{3}-2 a^{3} m^{5}} \]

✓ Solution by Mathematica

Time used: 0.651 (sec). Leaf size: 73

DSolve[D[y[x],{x,5}]-m^2*D[y[x],{x,3}]==Exp[a*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\frac {e^{a x}}{a^3}+\frac {(a-m) (a+m) \left (c_1 e^{m x}-c_2 e^{-m x}\right )}{m^3}}{(m-a) (a+m)}+c_5 x^2+c_4 x+c_3 \]