solve the initial-value problem
f''=e^(2x) where f(0)=4 and f'(0)=2
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(1 point) Solve the given initial value problem y′=2+e^(y−2x+4 ) y(0)=−4 The solution in the implicit form is F(x,y)=1, where F(x,y)= ? i had answer of this {y-ln(1/(-x+1))-2x+5}, don't know why its wrong.
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i, where f(t)-〈0 otherwise. (b) z', +x-f(t), x(0) 0, z'(0)=1, where t/2 if 0 t< 6, 3 ift26 f(t) 3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i,...
Please Answer 5-9 ALL in detail In problems 5 and 6 solve the given differential equation. 5. y (In x - In y) dx = (x In x - x In y - y) dy Ans: 6. (2x + y + 1) y' = 1 Ans: 7. Solve the initial-value problem + 2(t+1)y? = 0, y(0) = %. Ans: dy_y2 - xy(t) = -2. 8. Find an implicit solution of the initial-value problem 9. Ans: Use Euler's method sith step...
Please help me out with question 18. Its a question of laplace transfromation for unit step functions . thanks lems. Sketch a graph 14. F(s) = e-s (3) +e-> (5) Use Laplace transforms to solve the following initial value problems. Sketo the solution, together with a graph of the driving function. 15. x' + 2x = 2u(t - 3), x(0) = 1 16. x' + x = 2 + ut - 1)e-!, x(0) = 0 17. x" + 4x' +...
Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.) (x - 1)y" - xy + y = 0, 7(0) = -4, 7(0) = 2 y = 2x - 40 X
(1 point) Solve the given initial value problem y′=5+e^(y−5x+4) y(0)=−4 The solution in the implicit form is F(x,y)=1,, where F(x,y)=
(1) Solve the initial Value Problem (IVP): 2x+1 f'(x) = — ; f(0) = 1. x²+1 DE): frm=2* 31 (a) First, solve the differential equation (DE): f'(x) = 2x+1 — x2 + 1 1 2x+1 Hint: - x2+1 2 x 1 - + - x?+ 1 x2 + 1 2 x Guess a function whose derivative is x2 + 1x2+1 Gues humaian whose centraline a creative 1.a, tratan antarane element ;) 1 2 x 1 i.e., find an antiderivative of...
Use the Laplace transform to solve the given initial-value problem. 0 st<1 t 1 y' y f(t), y(0) 0, where f(t) (4, ae-1 -(1-1) 4 y(t) X Use the Laplace transform to solve the given initial-value problem. 0 st
please help with the question Solve the following initial value problem. y" – 9y' + 20y = 2x +€4x, y(0) = 0, y'(0) = 2
Answer all questions (especially part b if unable to do part a) QUESTION FOUR 25 MARKS] Consider the initial value problem d x()= A(0)x(t) +f(t), x(0) = xo where xo is some constant vector. A(T)dr A(t)= A(t)A()dr). Show that the matrix X (e) = ei A(0d (a) Assuming satisfies the matrix differential equation: Xt) = A(€)X(1) 10 Maris) (b) Obtain a solution to the initial value problem, given 0 A= f) x(0) -1 3 15 Marks QUESTION FOUR 25 MARKS]...