 , 22.06.2019 21:00 luzcastellanos556

# Find the general solution of the given differential equation. x dy dx − y = x2 sin(x) give the largest interval over which the general solution is defined. (think about the implications of any singular points. enter your answer using interval notation.  Divide both sides by . In doing so, we force any possible solutions to exist on either or (the "positive" interval in such a situation is usually taken over the "negative" one) because cannot be 0 in order for us to do this. Condense the left side as the derivative of a product, then integrate both sides and solve for :     Note that in order to do this division, we cannot allow . This means the largest interval on which a solution can exist is either or .

If is a solution to the ODE, then any term that vanishes as (or , depending on which interval above is used) is a transient term.

Solve the ODE: As , will oscillate between -1 and 1, so will oscillate between and , so the limit of as does not exists. There are no transient terms. Divide both sides by - note that this means we can't have :  Then the left side reduces to the derivative of a product,   This solution is continuous everywhere, but accounting for the singular point , the largest interval over which it is defined would be or .  ### Other questions on the subject: Mathematics Mathematics, 21.06.2019 19:00, Marleneg
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To solve the system of linear equations 8x+5y = 10 and 6x+y=-2 by using the linear combination method, amos decidedthat he should first multiply the second equation by –5 and then add the two equations together to eliminate the y-terms. hiscalculations are as shown. amos's solution is (2,-14). what did he do wrong? ​
Find the general solution of the given differential equation. x dy dx − y = x2 sin(x) give the large...

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