2. Solving a Separable Equation Example: Solve IVP: y' + et = e" sin t, y(T) = 0 Separate two variables t and y: put D.E. in form M(y)dy = N(t)dt Integrate each side w.r.t. t and y (Add C in one side.) • Find C' using y(ë) = 0. • Solve for y explicitly, if possible.

Q: Consider the Riccatti equation Please answer all parts. v'=v2-(7/x)v+8/x2 a) use the substitution…

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Q: Consider the Bernoulli equation y' + -y = 3y°. After applying an appropriate substitut this equation…

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Q: Euler Equation: t2y''+ty'+y=0, t>0

A: Here I am attaching image so that you understand each and every step.

Q: Exercise 1.5.5: Solve y' = (x + y − 1)². -

A: Answer:-

Q: 3. Find all solutions of the DE y"-12 y'+36 y=16 te (where t is a real constant) 6 x

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Q: Find y" if y = cot(9x 2r+ 8).

A: Given, y= cot(9x4-2x +8)   To find: y''

Q: 2. Differentiate the following equations. a. Differentiate. 11 y 1=22²2²² 7x²

A: Since we are given with the multiple  number of subpart  question answer will be according to the…

Q: 47. Show that y = x³ + 3x + 1 satisfies y"" + xy" - 2y = 0.

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Q: Consider the Riccatti equation v'=v2-(7/x)v+8/x2 a) use the substitution v=-y'/y

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Study the stability of the origin and plot some solutions for: x' = -2 1 X

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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.