Find the general solution of this DE, where a is a constant. Do not expand the...
(1) 5 - Yps Sp de - dx to find a second solution of the DE 3. Use the formula ya = yı 9 +2+y = 0, V1 = ce* 4. Find the general solution of each DE.
7. (10 points) Find the general solution to the homogeneous system of DE: x' = Ax where A = [-2 21
7. (10 points) Find the general solution to the homogeneous system of DE: -1 x' = Ax where A -2 = [ 21
dy 7. Determine the general solution to : x = x+y dx 8. Solve the DE (x - y)dx +(y – x)dy dy 9. Determine the general solution to : x? + 3xy = dx dy 10. Determine the general solution to : xy = 4x² + y2 dx 1 X
2 8. (10 points) Find the general solution to the homogeneous system of DE: | 3 x' = Ax where A = -2 1 - 1 -2 -4.
3. Verify that y1(x) x is a solution of Find the general solution of the DE on (0, 00).
1 -2 Find the general solution to the homogeneous system of DE: 3 2 6 x' = Ax where A = -2 1 -2
dy 2. Find the general solution of -y+e"y dv -6xy 3. Find the general solution of t dr 4y+9x2 dy dx Find the general solution of бх2e" + 4y. 4. 5. Find the general solution of dr (y +2) dy 5x +4y Find the general solution of dx 8y3 d By'-4x
Find the general solution to the non-homogeneous system of DE: -4 X+
Problem 1: Find the general solution for dx d?.x dt2 + 2k- + k.x = 0 dt where k is an arbitrary constant. Problem 2: Find a differential equation with solution -2.x -23 y = e cos(x) +e sin(x). Hint: Use the property that i2 = = -1 to simplify your work.