8.11.16 problem 31

Internal problem ID [884]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 31
Date solved : Wednesday, February 05, 2025 at 04:37:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

dsolve([diff(y(x),x$2)+4*y(x)=2*x,y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
 

\[ y = \frac {3 \sin \left (2 x \right )}{4}+\cos \left (2 x \right )+\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 22

DSolve[{D[y[x],{x,2}]+4*y[x]==2*x,{y[0]==1,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (2 x)+\frac {1}{2} (x+3 \sin (x) \cos (x)) \]