DiffEq  Practice Problems for Final Exam    -   Math 285   Fall 2011

 

 

 

 

 

1.

 

 

Draw several isoclines ( 3 to 4 ) of the equation   x y ‘ =  x2  +  y2

Answer:

 

 

 

2.

 

Let  y(x) be a solution to the initial value problem  xy ‘  =  e x+1 + sin y,   y(-1) = 0.

Find the tangent line to the graph of y(x) at  (-1,0).

 

       Answer:  y(x)  = - x - 1

 

 

 

3.

 

 

 

Is the equation   y ‘ sin(x/y) – (ln x) /( ln y)  =  cos(x/y)    separable, linear, Bernoulli,

homogeneous, none of these?

                                                         Answer:   None of these.

 

 

 

 

4.

 

 

Let  y(x) be a solution to the initial value problem  y ‘  =  2 x y  +  3 x2 exp(x2),  y(0) = 5.

Find the value of  y( -1 ).

                                                         Answer:  4 e

 

 

 

5.

 

Let  y(x) be a solution to the initial value problem  y ‘ =  x( 4 – x2 )/ y3,    y(1) = -2.

Find  y(0).
                        Answer:  - √3

 

 

 

6.

 

Find a general solution to the equation   x(x + 2y) y ‘  =  y (3x + y).

 

Answer:  y exp(2y/x)  =  C x3

 

 

 

7.

 

Find a general solution of the equation  y ‘’’  +  4 y ‘’  =  0

 

Answer:  y(x)  =  C1  +  C2 x  +  C3 e -4x

 

Click here to continue with this final exam.