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anonymous
 5 years ago
Differential equations:
y'=ycosx/sin^2x
ylnxxy'=o
7yy'5e^x=0
anonymous
 5 years ago
Differential equations: y'=ycosx/sin^2x ylnxxy'=o 7yy'5e^x=0

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01. separable 2. linear 3. separable

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you could use separable for all three: \[1) \frac{dy}{dx}=\frac{ycosx}{\sin^2x}\rightarrow \frac{dy}{y}=\frac{cosx}{\sin^2x}dx\] \[\int\limits_{}\frac{dy}{y}=\int\limits_{}\frac{cosx}{\sin^2x}dx \rightarrow lny=\frac{1}{sinx}+c\] use u substitution \[e^{lny}=e^{\frac{1}{sinx}+c}\rightarrow y=\frac{1}{e^{\frac{1}{sinx}}}+c\] \[2) ylnxx \frac{dy}{dx}=0\rightarrow \frac{dy}{y}=\frac{lnx}{x}dx\] \[\int\limits_{}\frac{dy}{y}=\int\limits_{}\frac{lnx}{x}dx \rightarrow lny=\frac{1}{2}(lnx)^2+c \rightarrow \] use u substitution \[e^{lny}=e^{((lnx)^2)^\frac{1}{2}+c}\rightarrow y=x+c\] \[3) 7y \frac{dy}{dx}5e^x=0\rightarrow 7ydy=5e^xdx \rightarrow \int\limits_{}7ydy=\int\limits_{}5e^xdx \rightarrow\] \[\frac{7}{2}y^2=5e^x+c \rightarrow y^2=\frac{10}{7}e^x+c \rightarrow y=\sqrt{\frac{10}{7}e^x+c}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nadeem: An excellent presentation. Very professional. May I ask you what software you use to effect that result. Thank you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks..... I used latex, the same software included in this website as an equation editor.
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