64.11.37 problem 37

Internal problem ID [13487]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 37
Date solved : Tuesday, January 28, 2025 at 05:45:37 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=3 x^{2}-4 \sin \left (x \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 23

dsolve([diff(y(x),x$2)+y(x)=3*x^2-4*sin(x),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = \left (2 x +6\right ) \cos \left (x \right )+3 x^{2}-\sin \left (x \right )-6 \]

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 112

DSolve[{D[y[x],{x,2}]+y[x]==3*x^2-4*Sin[x],{y[0]==0,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\cos (x) \int _1^0\sin (K[1]) \left (4 \sin (K[1])-3 K[1]^2\right )dK[1]+\cos (x) \int _1^x\sin (K[1]) \left (4 \sin (K[1])-3 K[1]^2\right )dK[1]+\sin (x) \left (\int _1^x\cos (K[2]) \left (3 K[2]^2-4 \sin (K[2])\right )dK[2]-\int _1^0\cos (K[2]) \left (3 K[2]^2-4 \sin (K[2])\right )dK[2]+1\right ) \]