Find the specific solution for the following ODE: dy = 2y dx Knowing that y (0) = 3

Q: Find the particular solution of the following ODE given that y(0)=0 and y'(0)=3: d'y dy +10 +25y = 0…

A: Explanation of the answer is as follows

Q: Solve the given ODE using the method of variation of parameters d²y dy 2x + 2у — х4 cos x dx2 dx

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Q: Find the particular solution of the given ODE. ( y − √x² + y²) dx − xdy = 0 when r = √3, y = 1 - -

A: This is homogeneous ordinary first order nonlinear differential equation

Q: *show work*

A: Find dy/dx.

Q: Q4) Find dy /dx for the following functions: a) e*y = x – y b) y = (cos x)Vx

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Q: Solve (1+x ) = x²y, given that x=1 when y = 2 dx Find the particular solution for y in terms of x.…

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Q: 6) Find dy given e 3y = y2 + x. opr dx

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Q: Solve the following second order ODE dy dy + 2x dx? = 0 || dx with the initial conditions y(0) = 2…

A: The given 2nd order ODE is d2ydx2+2xdydx2=0, with initial conditions y0=2 and y'0=-1. The main…

Q: Find dy/dx implicitly and find the largest interval of the form -a < y < a or 0 < y < a such that y…

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Q: Find the general solution of the given ODE ( 40² – v) dx + x dy 0.

A: The given DE is: (y2-y)dx+x dy=0⇒(y2-y)dx=-x…

Q: dy 1. Obtain from the following. dx 3at? y = 1+t3 3at x = (a is constant) 1+t3

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Q: Find the general solution of the given ODE. * (x + y – 1)dx – (x + y)dy= 0 -

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Q: If the D. E. + M(x, y))dx + sin(xy)dy = 0 is exact then the function М(х, у)

A: If the Differential Equation 1y+M(x,y)dx+sin(xy)dy=0 is exact then the function M(x,y)

Q: Find dy/dx implicitly and find the largest interval of the form -a < y < a or 0 < y < a such that y…

A: follow the procedure given below.

Q: dy = ( e )dx

A: See the attachment

Q: dy 5. If y = e+1 sin(1 – a2), then Find dx

A: We need to find the derivative of y=e3x+1sin1-x2 We will use the product rule to find the derivative…

Q: Find the particular solution of the following ODE given that y(0)=0 and y '(0)=0: d'y +y=e* dx

A: A Particular solution of the differential equation is a solution of the form y= f(x) , which don't…

Q: Find dy/dx implicitly and find the largest interval of the form -a <y <a or 0 < y <a such that y is…

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Q: Q2: Find the for the following functions: dy dx 1. y = 1- and t = 1/ 2. y [In(x² + 2)²1³ 3. y = xsex

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Q: dy x2 (b) Find the general solution to the DE cos? y dx

A: As per our guidelines only one question can be solved. Solution for "b" is given below in the next…

Q: Q1: Find dy/dx of the following functions: 1. x'e? y = log2 2Vx +1 2. (x - 2)*VI+5 y = Vx +4 y = t…

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Q: dy for the following implicit function at p(1,1) Find dx Vxy +1 = y is O 1 O 1/2 O -1/2

A: A detailed solution is given below.

Q: Find the solution of the following ODE: dy y + 1+x2 0, y(0) = 1 1- %3D dx

A: Apologies. We only answer one question at a time. We will answer question 1 as the exact one wasn't…

Q: Find the general solution of the ODE below. 2z y'" – 4y' + 4y = e" arcta y(x) =

A: Introduction: If a second-order homogeneous differential equation has two equal real roots, then the…

Q: Obtain dy from the following function y= e v*

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Q: Given x2 + 15x + 44 f( dx 1+ cos? (x) At what value of t does the local max of f(t) occur? F(4) = /…

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Q: Q11. For the ODE dy = (y cos(x) + 2x)/y ,y(0) = 0.8 dx %3! The most accurate answer when estimating…

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Q: Solve the first order o.d.e dy/dx=(1+y^2)e^x

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Q: Find the solution of the following ODE: dy 1- dx y = 0, y(0) = 1 1+x2

A: Linear differential equation is of the form dydx+Py=Q Where, P and Q are continuous function of 'x'…

Q: 181. y = (x + cos z) (1 – sin z sz)(

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Q: Solve the Following D.E x*dy = (z xy-j') dx %3D

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Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

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Q: d’y Q 3. Solve the ODE dx dy +6y = cos 3x using variation of parameter method. dx

A: given differential equation d2ydx2-5dydx+6y=cos3x

Q: find dz/dx and dz/dy for the following expression z =  tan-1 [(x+y)/(1-xy)]

A: This question is based on diffrentiation of function.

Q: Solve four questions of the following DEs 1- xy dy + (x? + y? )dy = 0 dx 2- 2 - y = e*/2 dy 3- (x +…

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Q: Find dy of the expression (xy)* = e %3D dx

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Q: Solve the following initial value problem for y as a function of x. dy x = /x? - 16, 3x dx x24, y(4)…

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Q: dy 4y dx

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Q: dy 1+y3 Determine the solution for the given DE: + = 0 dx xy?(1+x²)

A: Proceed as shown below

Q: dz dz 10. Compute for the following equation. and dx dy e*Y + xz? = 6xy*. *z° ||

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Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y ( 0) = 3

A: We can solve the given differential equation by using initial condition.

Q: Q2:B/ Find dy/dx f Via - "sin Vi dt y = + cos t dt

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Q: OBTAIN THE GENERAL SOLUTION 2. dx: t (1+e?) see" x dt 3. x dx - Ja - x² dy =0

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Q: dx Given y= e-2x? dy when X = 1 and dt 2. Determine the value of dt

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Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: Solve the Following D. E x*dy = (z xy-jJ dx %3D

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Q: Solve the following ODE numerically dx t3 – 2x -, for 1 <t< 3 with x = 4.2 at t = 1, t %| dt and…

A: Please see the below picture for detailed solution.