(3) Solve the exact initial value problem 1 √y+3 y(y + sin x) dx + 2xy - cos x + leaving the solution in implicit form. dy = 0, y(0) = 1,

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A: We solve the second-order non-homogeneous ordinary differential equation (ODE):y′′−3y′+2y=exusing…

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Q: Solve the general solution y" + y = xex sin 2x

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Q: (e – y cos (x)) dx + (2xes (ey – y (xy) + 2y) dy x Cos cos = 0 3.

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Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: 3. Solve (2 + 3x)² + 3(2 + 3x) -36y= ax² + bx + 1 + 2 sin ln(2 + 3x). dx²

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Q: Solve the initial value problem (3x² + y cos x)dx + (sin x - 4y³)dy = 0, y(0) = 2 Write the solution…

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Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: 2. Use method of undetermined coefficients to find general solution to the following equations: (a)…

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Q: 5. Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

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Q: (h) xy" + 8y' +18xy = 0, xo = 1 (i) (3 — x²)y" — 8xy' - 18y = 0, xo = 0 (j) 2y" + 8xy' + 18y = 0, xo…

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Q: Find the implicit solution of the differential equation (1+sin(y))dx + (1+x cos(y))dy = 0.

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Q: (b) Solve the following initial value problems: (2xy-9x²)+(x² + 2) t+2y-2 +3 sint; (1) = 0; y(0) = 3…

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Q: Find solution of equation 2 o(x) = 2f cos(x-1t) ø(1)dir

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Q: Determine the most appropriate method to find the general solution for the functions: y" - y' - 2y =…

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Q: Q7// find the general solution (sin-1x + 1 y)dx + sec-1xdy = 0 1 xVx² – |

A: The detailed solution is as follows below:

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Q: 6) solve The integral equation is He y(t) + 3 (= y(v) sin(t-v) dr = t The

A: Step 1: Given integral equation is y(t)+3∫0t​y(τ)sin(t−τ)dτ=t Step 2: Here the term…

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Q: (1 + t2)(dy/dt) + t · y = (1 + t2)5/2. Find general solution. SHOW ALL STEPS PLEASE. I DON'T KNOW…

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Q: c) Solve the initial value problem dx - x sin 2t = 2t² + 2t + 2, x(0) = 0 dt (1 + cos² t)-

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Q: Solve the initial value problem. (cosx)(dy/dx)+ysinx=6xcos2x, y(pi/3)=(-4pi2/3)

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