83.33.3 problem 3

Internal problem ID [19411]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (G) at page 115
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:38:47 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}-n^{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)-n^2*diff(y(x),x$3)=exp(a*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.632 (sec). Leaf size: 73

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

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