Internal problem ID [12425]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 2.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime \prime }+y^{\prime } x=4} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 1, y^{\prime \prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 49
dsolve([x*diff(y(x),x$3)+x*diff(y(x),x)=4,y(1) = 0, D(y)(1) = 1, (D@@2)(y)(1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \left (4 \,\operatorname {Ci}\left (1\right )-4 \,\operatorname {Ci}\left (x \right )+\cos \left (1\right )-\sin \left (1\right )\right ) \cos \left (x \right )+\left (4 \,\operatorname {Si}\left (1\right )-4 \,\operatorname {Si}\left (x \right )+\cos \left (1\right )+\sin \left (1\right )\right ) \sin \left (x \right )+4 \ln \left (x \right )-1 \]
✓ Solution by Mathematica
Time used: 0.184 (sec). Leaf size: 85
DSolve[{x*y'''[x]+x*y'[x]==4,{y[1]==0,y'[1]==1,y''[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -4 \operatorname {CosIntegral}(x) \cos (x)+4 \operatorname {CosIntegral}(1) \cos (x)-2 \text {sinc}(1) \cos (2-x)-6 \text {sinc}(1) \cos (x)+8 \text {sinc}(1) \cos (1)-4 \text {Si}(x) \sin (x)+4 \text {Si}(1) \sin (x)+4 \log (x)+\sin (1-x)+\sin (3-x)+3 \sin (x+1)+\cos (1-x)-1-4 \sin (2) \]