12.20.15 problem section 9.4, problem 36

Internal problem ID [2236]
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 36
Date solved : Monday, January 27, 2025 at 05:43:55 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&=F \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(x^3*diff(y(x),x$3)+x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=F(x),y(x), singsol=all)
 

\[ y = \left (c_3 +\int \frac {c_2 +\int \frac {c_1 +\int F \left (x \right )d x}{x^{3}}d x}{x^{2}}d x \right ) x^{2} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 82

DSolve[x^3*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+2*y[x]==f[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3 \int _1^x\frac {f(K[3])}{3 K[3]^3}dK[3]+x^2 \int _1^x-\frac {f(K[2])}{2 K[2]^2}dK[2]+\int _1^x\frac {1}{6} f(K[1])dK[1]+c_3 x^3+c_2 x^2+c_1}{x} \]