Find the function y1 of t which is the solution of 121y′′+88y′+12y=0 with initial conditions y1(0)=1,y′1(0)=0. Find the function y2 of t which is the solution of 121y′′+88y′+12y=0 with initial conditions y2(0)=0,y′2(0)=1. Find the Wronskian W(t)=W(y1,y2).

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Q: (5) Consider the Adams-Bashforth method wo = a; wi = ɑ1; Wi+1 = Wi + [3f (ti, wi) – f(ii-1, wi–1)]…

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Q: (5) Consider the Adams-Bashforth method wo = a; wi = a1; Wi+1 = Wi + 5 (3f(t;, wi) – f(i;-1, Wi-1)]…

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Q: 2. (a) Find the general solution of the PDE y²ur + x²uy = 2xy² (b) Find the solution, if it exists,…

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Q: Find y as a function of t if y" + y' – 2y = 0, y(0) = 8, y(1) = 8. y(t) = Remark: The initial…

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Q: -19s + 24 a) L{y(t)} = s2 b) L {y(t)} = 17s+20 s2 -21s + 28 c) L {y(t)} = s2 -15s + 22 d) L {y(t)} =…

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Q: Find y as a function of t if y" – 10y' + 21y = 0, y(0) = 7, y(1) = 4. y(t) = Remark: The initial…

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Q: A second order Caushy – Euler equation having a solution y(x) = x-2cos(4Inx) is x?y" + 5xy' = 0 O…

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Q: EXAMPLE 5 Show that y1(t) = t1/2 and y2(t) = t−1 form a fundamental set of solutions of (14)…

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Q: Consider the linear ODE *'y() + 6a?y" + 4®y/ – 4y = 0 (a) Verify that y1 = *, 2 = -2 and y3 = -2 In…

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Q: • Verify that 3r is a one-parameter family of solutions of the DE ry + y = 3r. • Deduce a solution…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.