Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 – 8) dy = 0, y(1) = 1 (x + y)3 (x + y)2 - 8x = -1
Solve the initial value problem (2x – y2)dx + (1 – 2xy)dy = 0, y(1) = 5
29. (a) Without solving, explain why the initial-value problem dy dx vy, y(xo) = yo has no solution for yo < 0. (b) Solve the initial-value problem in part (a) for yo > 0 and find the largest interval / on which the solution is defined
38. Solve the initial value problem x+3y=+*2 + 2xy +T Y() = -2 2xy x2 + 2x2y + 1 Ti y(1) = -2.
Solve the following Initial value problem over the Interval from t-0 to 2 where yo)-1 using the following methods dy= yt2_ 1.1y 5. value 15.00 points Fourth-order RK method with h- 0.5 at t-2 O 0.5914 O 1.5845 O 2.7332 O 0.7614
4. Solve the exact differential equation. (1-2xy)dx + (4y3 - x2)dy 0
4. Solve the exact differential equation. (1-2xy)dx + (4y3 - x2)dy 0
2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7 points) Find all critical points and the phase portrait of the autonomous Ist order ODE dy dr -5y+4 Classify each critical point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves in the regions in the ry plane separated by equilibrium solutions. dy dx (S points) Solve the Bernoulli equation:-(- 31-1 7. (8 points) Solve the ODE by variation of parameters: -4y+4y (+...
dy 1.A. Solve the differential equation: = = y2ex dx dy B. Solve the initial value problem: + 2y = 3x2 ; y(0) = 1 dx C.A certain radioactive substance has a half life of 1300 years. Assume an amount yo was initially present. a.Find a formula for the amount of radioactive substance present at any time t. b.In how many years will only 1/10 of the original amount remain?
Solve the initial value problem dy dx+2y-4e0y(O)2 The solution is y(x)
Solve the initial value problem dy dx+2y-4e0y(O)2 The solution is y(x)
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo . and for yo > Ye, (a) Find the critical value of yo, yc, such that for yo < yc, limt 400 y(t) = - limt700 y(t) = 0. (b) What happens if yo = ye?