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Differential Equations by Separation of Variables - Classwork dy ! f ( x ) ! g( y ) . In order to solve it, you must put it in the form of dx g( y ) ! dy ! f ( x ) ! dx allowing you to integrate. Your goal is to get an equation in the form of y ! h ( x ) dy 2 x dy dy x $ sin( x ) 1) 3) ! 2) ! y2 ! 3y 2 dx y dx dx A differential equation will be in the form of 4) dy ! 4y dx 7. du ! e u $2 t dt 5. dy ! ky dx 6) 8. dy ! xy dx dx ! 1 $ t " x " tx dt Find the solution of the differential equation that satisfies the given condition. dx dy 1 $ x ! 1 , x (0) ! 1 10. , y (1) ! "4 9. xe" t ! dt dx xy 11. dy ! y 2 $ 1 , y (1) ! 0 dx MasterMathMentor.com 12. x $ 2 y x 2 $ 1 - 212 - dy ! 0 , y (0) ! 1 dx Stu Schwartz Differential Equations by Separation of Variables - Homework 1. dy x ! dx y 3. x dy !y dx 2. dy x 2 $ 2 ! dx 3y 2 4. (2 $ x ) dy ! 3y dx 6. (1 $ 4 x 2 ) y # ! 1 5. yy # ! sin x Find the solution of the differential equation that satisfies the given condition. dy dy ! 0 , y (1) ! 4 8. y ! e x , y (0) ! 4 7. x $ y dx dx 9. xy dy " ln x ! 0 , y (1) ! 0 dx 11. (1 $ x 2 ) 10. y ( x $ 1) $ dy " (1 + y 2 ) ! 0 , y (0) ! 3 dx MasterMathMentor.com dy ! 0 , y ("2) ! 1 dx 12. dT $ k (T " 70) dt ! 0 , T (0) ! 140 - 213 - Stu Schwartz