) Solve ke 0.D.E using Eiga valus/ Eiga vecters dt - 3 1-1 coher = cwher 7= A = 3 -1 || 1 33 F = (3)e", 7n = ( 2t

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Q: Find the value of ds / du at u = 2 if s = t2 + 5t andt = (u2 + 2u)1/3.

A: We first find ds/dt and dt/du

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Q: Find the solution of the initial condition problem: j + t°ÿ+ 3t?y = 0, , y(0) = 1, ý(0) = -1. |

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

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A: Given that, ay'-by=kcoscx+mx,   y(0)=5∆x=0.025a=2, b=4, k=6, c=2 and m=7We need to find y0.2 using…

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A: The detailed solution is given below Thank you

Q: Evaluate the integrals

A: 37. ∫112142dtt+4tt38. ∫0edyy1+(ln y)2

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A: In this question , we can solve for 'd'.

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Q: EX Use Euler's method ( modified) to approx; mat e y' = x+y for yC1) = 1; h=o.1,13X<z withe aecuracy…

A: We Use here Euler's Modified Method to find the solution.

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Q: Q4/is that, the Sulutton to the differentiel equation dy-tX+4. is it's

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Q: Solve the initial-value problem. du = t? + 3u, dt t > 0, u(4) = 48 %3D

A: Recall: First order differential equation : Consider the differential equation…

Q: 2. J고dr (e* -1) (e +1)

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A: Given, The differential equation  xcosxdx+1-6ydy=0   ;  yπ=0 We have to solve it.

Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

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Q: 2 2 dx using Mid – Point Rule is The approximation of o x²- 4 | 1 15 16 15 14 15 None of these 8 15

A: The given integration is,∫022x2-4 dxSo, here f(x)=2x2-4

Q: 1.2 Exercises a. Show that ¢ (x) = x2 is an explicit solution to 1. dy = 2y dx

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Q: Use Euler method to approximate the value of y(0.2), given ay' - by = kcos(cx) + mx , y(0) = 9 with…

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Q: b. Obtain the particular solution of the following dr =-4rt; when t=0, r =r, dt i.

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Q: Verify that u(z, t) = f(e'r) solves the initial value problem (a,u + z8,u = 0, u(x,0) = f(x).

A: Take the partial derivatives of u(x,t).

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A: solution of non differential equation

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Q: 7. Given paths ri(t) = (t², t°, t) and r2(t) = (In(t), e2t, In(3t)) compute the following…

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A: D'Alembert Solution;    u(x,t)=ux,t=12f(x+ct)+f(x-ct)+12c∫x-ctx+ctg(ξ)dξ where u(x,0)=f(x),…

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Q: Solve the following initial value problem: dy t + dt 3y² (³,²-1²): y(t)= -55/366 2y4 = 0, y(1) = 3.…

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Q: Obtain the particular solution satisfying the indicated condition. lnx/e^ydy=xdy ; y(1)=0

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Q: dy When solving the Bernoulli DE: x - = , which of the choices is utilized for (1+x²)y substitution…

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