Show that the differential equations is linear and solve for thegeneral solutions. h.dxdym2y == czem1x where c1, m1, m2 are constants & m1 ± m2

For a differential equation of the form, dydx+P(x)y=Q(x) , the integrating factor is defined as…

Answered: dy тгу 3 С1е"1* where c1, m, тz are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear. Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear: 2 ? ? 2 V 1. y" -y + y² = 0 2 3. d²y + sin(t + y) = sint dt² d¹y d³y d²y dy + + dt4 dt³ dt² dt d²y dy dt dt² 4. (1+²) +t + = 1 +y=et
I would like this problem to be solved via Differential Equations. Thank you!Suppose you cool a pot of soup in a 75 °F room. Right when you take the soup off the stove, you measure its temperature to be 220 °F. Suppose after 20 minutes, the soup has cooled to 170 °F. Suppose you can eat the soup when it is 130 °F. How long will it take to cool to this temperature?
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It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involed) and whether or not the equation is linear. Linearity is important because the structure of the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear for 2 3 and 4 it is also based on the drop down menu (in the picture)

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dy тгу 3 С1е"1* where c1, m, тz are constants & mi # m2 dx