Internal problem ID [12744]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 y^{\prime \prime }-2 y^{\prime }+4 y=x} \] With initial conditions \begin {align*} [y \left (-1\right ) = 2, y^{\prime }\left (-1\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 85
dsolve([3*diff(y(x),x$2)-2*diff(y(x),x)+4*y(x)=x,y(-1) = 2, D(y)(-1) = 3],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (49 \sin \left (\frac {\sqrt {11}}{3}\right ) \sqrt {11}+187 \cos \left (\frac {\sqrt {11}}{3}\right )\right ) \cos \left (\frac {\sqrt {11}\, x}{3}\right )+49 \sin \left (\frac {\sqrt {11}\, x}{3}\right ) \left (\cos \left (\frac {\sqrt {11}}{3}\right ) \sqrt {11}-\frac {187 \sin \left (\frac {\sqrt {11}}{3}\right )}{49}\right )\right ) {\mathrm e}^{\frac {x}{3}+\frac {1}{3}}}{88}+\frac {x}{4}+\frac {1}{8} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 67
DSolve[{3*y''[x]-2*y'[x]+4*y[x]==x,{y[-1]==2,y'[-1]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{88} \left (22 x+49 \sqrt {11} e^{\frac {x+1}{3}} \sin \left (\frac {1}{3} \sqrt {11} (x+1)\right )+187 e^{\frac {x+1}{3}} \cos \left (\frac {1}{3} \sqrt {11} (x+1)\right )+11\right ) \]