35.6.27 problem 33

Internal problem ID [6177]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 33
Date solved : Monday, January 27, 2025 at 01:46:40 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)+y(x)=x^3-1+2*cos(x)+(2-4*x)*exp(x),y(x), singsol=all)
 

\[ y = \left (c_1 +1\right ) \cos \left (x \right )+\left (-2 x +3\right ) {\mathrm e}^{x}+\left (c_2 +x \right ) \sin \left (x \right )+x^{3}-6 x -1 \]

✓ Solution by Mathematica

Time used: 0.525 (sec). Leaf size: 40

DSolve[D[y[x],{x,2}]+y[x]==x^3-1+2*Cos[x]+(2-4*x)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3-2 e^x x-6 x+3 e^x+\left (\frac {1}{2}+c_1\right ) \cos (x)+(x+c_2) \sin (x)-1 \]