12.20.10 problem section 9.4, problem 27

Internal problem ID [2231]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
Problem number : section 9.4, problem 27
Date solved : Monday, January 27, 2025 at 05:43:51 AM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (-1\right )&=-6\\ y^{\prime }\left (-1\right )&={\frac {43}{6}}\\ y^{\prime \prime }\left (-1\right )&=-{\frac {5}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 28

dsolve([x^3*diff(y(x),x$3)+x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=x*(x+1),y(-1) = -6, D(y)(-1) = 43/6, (D@@2)(y)(-1) = -5/2],y(x), singsol=all)
 

\[ y = \frac {x \left (-2 i \pi x +2 x \ln \left (x \right )+3 i \pi -3 \ln \left (x \right )-12 x +24\right )}{6} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 34

DSolve[{x^3*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+2*y[x]==x*(x+1),{y[-1]==-6,Derivative[1][y][-1]==43/6,Derivative[2][y][-1]==-5/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} x (-2 i \pi x-12 x+(2 x-3) \log (x)+3 i \pi +24) \]