71.9.1 problem 1

Internal problem ID [14480]
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
Date solved : Tuesday, January 28, 2025 at 06:41:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (-1\right )&=2\\ y^{\prime }\left (-1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.420 (sec). Leaf size: 74

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)
 

\[ y = \frac {\left (\left (49 \sin \left (\frac {\sqrt {11}}{3}\right ) \sqrt {11}+187 \cos \left (\frac {\sqrt {11}}{3}\right )\right ) \cos \left (\frac {\sqrt {11}\, x}{3}\right )+49 \sin \left (\frac {\sqrt {11}\, x}{3}\right ) \left (\cos \left (\frac {\sqrt {11}}{3}\right ) \sqrt {11}-\frac {187 \sin \left (\frac {\sqrt {11}}{3}\right )}{49}\right )\right ) {\mathrm e}^{\frac {x}{3}+\frac {1}{3}}}{88}+\frac {x}{4}+\frac {1}{8} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 67

DSolve[{3*D[y[x],{x,2}]-2*D[y[x],x]+4*y[x]==x,{y[-1]==2,Derivative[1][y][-1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{88} \left (22 x+49 \sqrt {11} e^{\frac {x+1}{3}} \sin \left (\frac {1}{3} \sqrt {11} (x+1)\right )+187 e^{\frac {x+1}{3}} \cos \left (\frac {1}{3} \sqrt {11} (x+1)\right )+11\right ) \]