82.33.8 problem Ex. 8

Internal problem ID [18901]
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. 8
Date solved : Tuesday, January 28, 2025 at 12:34:02 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \left (b x +a \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 78

dsolve(diff(y(x),x$4)+diff(y(x),x$3)+diff(y(x),x$2)=x^2*(a+b*x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {{\mathrm e}^{-\frac {x}{2}} \left (-\sqrt {3}\, c_{2} +c_{1} \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )}{2}-\frac {{\mathrm e}^{-\frac {x}{2}} \left (\sqrt {3}\, c_{1} +c_{2} \right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )}{2}+\frac {b \,x^{5}}{20}+\frac {\left (a -3 b \right ) x^{4}}{12}-\frac {a \,x^{3}}{3}+3 b \,x^{2}+c_3 x +c_4 \]

✓ Solution by Mathematica

Time used: 0.961 (sec). Leaf size: 107

DSolve[D[y[x],{x,4}]+D[y[x],{x,3}]+D[y[x],{x,2}]==x^2*(a+b*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} \left (a (x-4) x^3+\frac {3}{5} b \left (x^3-5 x^2+60\right ) x^2+6 \left (\sqrt {3} c_1-c_2\right ) e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )-6 \left (c_1+\sqrt {3} c_2\right ) e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )\right )+c_4 x+c_3 \]