15.11.33 problem 33

Internal problem ID [3143]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 33
Date solved : Monday, January 27, 2025 at 07:23:29 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}}\\ y^{\prime }\left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 34

dsolve([2*diff(y(x),x$2)+5*diff(y(x),x)-3*y(x)=sin(x)-8*x,y(0) = 1/2, D(y)(0) = 1/2],y(x), singsol=all)
 

\[ y = \frac {8 \left (-\frac {51 \,{\mathrm e}^{\frac {7 x}{2}}}{35}+\frac {13}{840}+\left (x -\frac {3 \cos \left (x \right )}{80}-\frac {3 \sin \left (x \right )}{80}+\frac {5}{3}\right ) {\mathrm e}^{3 x}\right ) {\mathrm e}^{-3 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 38

DSolve[{2*D[y[x],{x,2}]+5*D[y[x],x]-3*y[x]==Sin[x]-8*x,{y[0]==1/2,Derivative[1][y][0] ==1/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{630} \left (1680 x+26 e^{-3 x}-2448 e^{x/2}-63 \sin (x)-63 \cos (x)+2800\right ) \]