62.29.4 problem Ex 5

Internal problem ID [12955]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary. Page 117
Problem number : Ex 5
Date solved : Tuesday, January 28, 2025 at 04:45:16 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime }&=x^{2}-3 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 35

dsolve(diff(y(x),x$3)-4*diff(y(x),x)=x^2-3*exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (9-12 x +16 c_{1} \right ) {\mathrm e}^{2 x}}{32}-\frac {x^{3}}{12}-\frac {c_{2} {\mathrm e}^{-2 x}}{2}-\frac {x}{8}+c_3 \]

✓ Solution by Mathematica

Time used: 12.586 (sec). Leaf size: 99

DSolve[D[y[x],{x,3}]-4*D[y[x],x]==x^2-3*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-2 K[3]} \left (e^{4 K[3]} c_1+c_2+e^{4 K[3]} \int _1^{K[3]}\frac {1}{4} \left (e^{-2 K[1]} K[1]^2-3\right )dK[1]+\int _1^{K[3]}\left (\frac {3}{4} e^{4 K[2]}-\frac {1}{4} e^{2 K[2]} K[2]^2\right )dK[2]\right )dK[3]+c_3 \]