62.27.6 problem Ex 6

Internal problem ID [12944]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of undetermined coefficients. Page 107
Problem number : Ex 6
Date solved : Tuesday, January 28, 2025 at 04:44:45 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }&=3 x^{2}+\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

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

\[ y = -\frac {x^{3}}{3}+\frac {2 x^{2}}{3}-c_{2} {\mathrm e}^{-x}+\frac {{\mathrm e}^{3 x} c_{1}}{3}+\frac {\sin \left (x \right )}{10}+\frac {\cos \left (x \right )}{5}-\frac {14 x}{9}+c_3 \]

✓ Solution by Mathematica

Time used: 27.194 (sec). Leaf size: 95

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

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