siriusmart@lemmy.worldM to Daily Maths Challenges@lemmy.world · 7 months ago[2024/05/14] General differential equationlemmy.worldimagemessage-square3fedilinkarrow-up19arrow-down10file-text
arrow-up19arrow-down1image[2024/05/14] General differential equationlemmy.worldsiriusmart@lemmy.worldM to Daily Maths Challenges@lemmy.world · 7 months agomessage-square3fedilinkfile-text
minus-squarezkfcfbzr@lemmy.worldlinkfedilinkEnglisharrow-up3·edit-27 months ago solution Not sure if I’d have gotten this one without Cavy’s hint, I’m pretty bad with differential equations Let z = ln(y) Then z = dy/dx / y dy/dx / y is the derivative of ln(y) So we have z = d/dx ln(y), or ln(y) = d/dx ln(y) ln(y) is its own derivative - so we must have ln(y) = e^x, which implies y = e^(e^x)
solution
Not sure if I’d have gotten this one without Cavy’s hint, I’m pretty bad with differential equations
Let z = ln(y)
Then z = dy/dx / y
dy/dx / y is the derivative of ln(y)
So we have z = d/dx ln(y), or ln(y) = d/dx ln(y)
ln(y) is its own derivative - so we must have ln(y) = e^x, which implies y = e^(e^x)