Can you show me a simple step by step method on how to solve these two problems:   1. Solve y′ = 1−y^2/x and determine the solution that satisfies y(1) = 0. 2. Solve y′ = y ln(y) with the initial condition y(1) = e.

Q: If y=-2x² + sin x solve for the differential of dy.

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Q: Q33. Solve the differential equation 5 xz (a) y3 = +c 5 (b) y³ = + c 1 x√x 5 (c) y³ = √x + c< 5 5…

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Q: Find a particular solution to the equation Yp(x) = y'' + 8y' + 16y= = e 4x arctant

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Q: 3. Solve each equation. y(0) = 1, y' (0) = -1 (a) y" + 4y = 0, (b) y" + 5y = 0

A: We have to solve given problem:

Q: The general solution of y' = 10 can be written in the form Y =C D

A: We are solving the given problem by using the method of separation of variable.

Q: 4. Solve the following DE: (2x²y)y' = x³ + 2y³

A: Given in the question, The diffrential equation is as follows:- By dividing both sides by 2x2 * y3,…

Q: Solve the following Clairaut equation   y=xy'+(y')^2

A: Firstly we will differentiate this equation to get simpler differential equation

Q: Solve the following IVP y' = e- (2x - 4) dr de == y(5) = 0 r(1) = 2

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Q: Solve the given differential equation. x?y" - 12y = 0 +V7 Y(x) =

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Q: 5. A differential equation is if it can be written in the form f(y)d(y) = g(x)d(x)-

A: A differential equation is ORDINARY if it can be  Written in the form f(y)dy = g(x) dx .

Q: 29. If f(x) = 0.5x³-x + 5 and g(x) = f'(x), find g'(7). B. 1/4 A. 1/7 C) 1/5

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Q: f y=y(x) is the desired solution of 2 = f(x,y), Derive Euler %3D teration formula for solving ODES…

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Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

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Q: Solve the following IVP: (7et '+ 9y = {o if 0 5 y'(0) = -1. %3D y(0) = 0, Note: Write your final…

A: The solution is given below

Q: Solve the following IVP y' = e(2x - 4) y(5) = 0 O ev = x² - x - 4 2 2 ey = x² - 4x − 4 T ex = y² -…

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Q: 5. Solve the equation y-y'y"=1, given that y=√2 and y'- and y'= when r=0.

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Q: Solve the equation y" + 36y= exp(2x) where y(0) = y'(0) = 0.

A: Given: y"+36y=exp(2x); y0=y'0=0To find: yx

Q: Q4. Solve numerically xy"+y' + xy = 0 with y(1) = 0.7652, y'(1) = -0.44 and h = 0.25 (do 4…

A: xy''+y'+xy=0y1=0.7652y'1=-0.44h=0.25

Q: SOLVE FOR THE EXACT DIFFERENTIAL EQUATION: (e4* + 2xy²)dx + (cos y + 2x²y)dy = 0 %D

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