1. Use Euler iterative technique to solve = (xy)² for y(0)=2 with h=0.5, find y(2) dx

Q: (a) Write the equation in slope-intercept form, and determine the slope and y-intercept. (b) Graph…

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Q: Use Picard's method to solve dx - Find y3(1)? -xy, y (0) = 1

A: Solution :-

Q: (2xy + 3y²) dx – (2xy + x²) dy = 0 .. [VARIABLE SEPARABLE/HOMOGENEOUS |

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Q: d'x +x=f(t), if x =x' = 0 for t = 0. Solve d?

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Q: Q2: find y' y= 33xelnx2

A: y=33xelnx2 We know that elnx2=x2 Now ,y'=33xx2 Differentiate using the product rule…

Q: Solve the D.E y' 1 (e-y-x)

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Q: Solve the ODE  y'+(1/x)y-ex=0, when x>0

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Q: Solve the equation y' + 3y = 10 sint, when y(0) two decimal place number. 0. Evaluate f (1) in

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Q: A solid concrete porch consists of 3 steps and a landing. The steps have a tread of 11 inches, a…

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Q: Solve: x"(t) + 2x'(t) + x(t) = 3t e-t x(0) = 4, x'(0) = 2 Evaluate: F(2) = Evaluate: f(1) =…

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Q: Find y' and y". y' y" = y = (²+ √x)³ 3

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Q: Find dy/dx if y = e-(1/10)e-x/2.

A: Given: y=e-110e-x2. To find dydx. Solution: Chain rule of differentiation states that:…

Q: 4. Use variation of parameters m y"+y' = ln x

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Q: Question 6 Prior to running the Boston Marathon, a runner's personal best pace for a race is 10…

A: Given that Prior to running the Boston Marathon, a runner’s personal best pace for a race is 10…

Q: dy Q.2 Solve x/1+ y² + yv1 +x² = 0. dx

A: The expression is x1+y2+y1+x2dydx=0 Multiply both sides by 11+x2·1+y2…

Q: x' = 10 t² x², x(0) = 3 Solve the above IVP and then find x(0.5). Put x(0.5) accurately calculated…

A: Given differential equation is, x'=10t2x2, x0=3.

Q: Solve the Bernoulli's DE: 2x3 y = y(y? + 3x2). %3D

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Q: Runge-Kutta 4th

A: y' = y-x   , y(0) =2here h = 0.1f(x , y ) = y-xx0=0y0= 2y(0.1) = y(0) +16(k1+2k2+2k3+k4)k1 = (0.1)…

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: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

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Q: Solve: y'(t)=1-sint –[ »(r)dr; y(0)=0,

A: We will find out the required solution for given differential equation using Laplace transform…

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.