Math 2233Homework Set 81. Determine the lower bound for the radius of convergence of series solutions about each given pointxo.(a)y+4y+6xy=0,x0=0(b) (x-1)y+xyxyx0=4(c)(4+x2)yxy+yx0(d)(1+x2)yxy+yx0=22. Determine the singular points of the following differential equations and state whether they are regularor irregular singular points.(a)xy+(1-x)y+xy(b)x2(1-x)2y+2xyy(c) (1-x2)2y+x(1-x)y+(1+x)y3. Compute the Laplace transform of the following functions.(a)f(t)=t(b)f(ttn4. Use the Laplace transform to solve the given initial value problem.
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