81.6.12 problem 12

Internal problem ID [18695]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 12:10:39 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} \left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve((x+3*x^2)*diff(y(x),x$2)+2*(1+6*x)*diff(y(x),x)+6*y(x)=sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{2} +c_{1} x -\sin \left (x \right )}{3 x^{2}+x} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 26

DSolve[(x+3*x^2)*D[y[x],{x,2}]+2*(1+6*x)*D[y[x],x]+6*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-\sin (x)+c_2 x+c_1}{3 x^2+x} \]