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2. Solve (i) Find the general solution of y" + y' = 0. Here, don't have...
Solve the initial value problem: y''-2y'+y=0, y(0)=2, y'(0)=1 . A) Write its characteristic equation. B) Write a fundamental set of solutions of the homogenous equation. C) Prove that your solutions from B) are independent. D) Find the solution satisfying initial conditions.
(1 point) The general solution of the homogeneous differential equation can be written as 2 where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation 2y 5ryy 18z+1 isyp so yax-1+bx-5+1+3x NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) 3, y'(1) 8 The fundamental theorem for linear IVPs shows that this solution is the unique solution to...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
6. [0/2 points) DETAILS PREVIOUS ANSWERS Find the general (real) solution of the differential equation: y"- 2y'- 15y=-51 sin(3 x) -3x | Ae 5x + Be 34 y(x) = 8.5 + -cos(3x) * 17 51 14 sin(3x) - - Find the unique solution that satisfies the initial conditions: Y(0) = 2.5 and y'(o)=37 y(x) = 7. [-12 Points) DETAILS Find the general (real) solution of the differential equation: y" + 4y' + 4y=64 cos(2x) y(x) = Find the unique solution...
(c) (i) Find the general solution of the following partial differential equation y, = 2y sin x + e-x Whatische solution when the initial conditions are v(0,y)--y, and (ii) y(x, 0) = cos x ? (10 Marks)
Q5) Find a general solution. Check your answer by substitution. 4y" – 25y = 0 y" + 36y = 0 y" + 6y' + 8.96y = 0) y" + 2k%y' + k4y = 0 Q6) Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. y" + 25y = 0, y(0) = 4.6, y'(0) = -1.2 4y" – 4y' – 3y = 0, y(-2) = e, y'(-2) =...
y' = f(y, t), y(t0) = y0. (i) what conditions guaranteeing a unique solution to the nonlinear initial value problem (ii) After checking the conditions, state what the theorem predicts for the initial value problem y' = (-x2 )/y , y(1) = 0. (iii) Solve the above initial value problem and find two distinct solutions (iv) Explain if results in (iii) and in (ii) contradict each other
4. Given that {cos x, sin 2, 1) is a fundamental set of solutions for y" + y = 0, solve the initial value problem with conditions y(0) = 3, y'(0) = 5, "(0) = -4. 4. Given that {coso, sin x 1} is a fundamental set of solutions for y'" + y = 0, solve the initial value problem with conditions y(0) - 3, V'(0) -- 5. "(0) -4
(17 points) (a) Find the general solution of the differential equation y" (t) + 4y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (i) y(0) = 0, y'(0) = 1: y = (ii) y(0) = 1, y'(0) = 0:y= (iii) y(0) = 1, y(1) = 0:y= (iv) y(0) = 0, y(1) = 1: y = (On a...
Two solutions to y' + 6y + 25 = 0 are y1 = = e 3t sin(4t), y2 = e cos( 4t). a) Find the Wronskian. W b) Find the solution satisfying the initial conditions y(0) = - 4, y'(0) = 0 y =